The 13th to 15th Amendments to the U.S. Constitution are called the "civil war amendments" as they were enacted in the fallout from the U.S. Civil War.
The 15th Amendment specifically addresses racial discrimination in voting rights, which was emerging as an issue a federal occupation of Southern states was receding and the segregation regimes that persisted until the 1960s, almost a century later, replaced slavery (which was abolished, de jure, and to a great extent, in practice).
The 13th Amendment abolishing slavery, comes very close, because at the time that it was adopted, slavery was almost exclusively imposed on African-Americans (the Emancipation Proclamation during the Civil War was the proximate legal cause of ending slavery for most U.S. slaves, although it took a fair amount of time to be fully implemented because the U.S. did not control much of the territory it applied to at the time).
The 14th Amendment was also race conscious, not by its express text, but by what is displaced. Section 1 removed the denial of citizenship for former slaves (an almost entirely African-American population), and expressly required the state to afford the new citizens equal protection of the laws and due process. Section 2 removed the three-fifths compromise from Congressional apportionment that had counted African-American slaves as less than a full person in the pre-14th Amendment status quo. Section 4 invalidated efforts to pay reparations to former slave owners.
Specifically, they state:
13th Amendment
Section 1 Neither slavery nor involuntary servitude, except as a
punishment for crime whereof the party shall have been duly convicted,
shall exist within the United States, or any place subject to their jurisdiction.
Section 2 Congress shall have power to enforce this article by
appropriate legislation.
14th Amendment Section 1 All persons born or naturalized in the
United States, and subject to the jurisdiction thereof, are citizens
of the United States and of the State wherein they reside. No State
shall make or enforce any law which shall abridge the privileges or
immunities of citizens of the United States; nor shall any State
deprive any person of life, liberty, or property, without due process
of law; nor deny to any person within its jurisdiction the equal
protection of the laws.
Section 2 Representatives shall be apportioned among the several
States according to their respective numbers, counting the whole
number of persons in each State, excluding Indians not taxed. But
when the right to vote at any election for the choice of electors for
President and Vice-President of the United States, Representatives in
Congress, the Executive and Judicial officers of a State, or the
members of the Legislature thereof, is denied to any of the male
inhabitants of such State, being twenty-one years of age, and citizens
of the United States, or in any way abridged, except for participation
in rebellion, or other crime, the basis of representation therein
shall be reduced in the proportion which the number of such male
citizens shall bear to the whole number of male citizens twenty-one
years of age in such State.
Section 3 No person shall be a Senator or Representative in Congress,
or elector of President and Vice-President, or hold any office, civil
or military, under the United States, or under any State, who, having
previously taken an oath, as a member of Congress, or as an officer of
the United States, or as a member of any State legislature, or as an
executive or judicial officer of any State, to support the
Constitution of the United States, shall have engaged in insurrection
or rebellion against the same, or given aid or comfort to the enemies
thereof. But Congress may by a vote of two-thirds of each House,
remove such disability.
Section 4 The validity of the public debt of the United States,
authorized by law, including debts incurred for payment of pensions
and bounties for services in suppressing insurrection or rebellion,
shall not be questioned. But neither the United States nor any State
shall assume or pay any debt or obligation incurred in aid of
insurrection or rebellion against the United States, or any claim
for the loss or emancipation of any slave; but all such debts,
obligations and claims shall be held illegal and void.
Section 5 The Congress shall have the power to enforce, by appropriate
legislation, the provisions of this article.
15th Amendment
Section 1 The right of citizens of the United States to vote shall
not be denied or abridged by the United States or by any State on
account of race, color, or previous condition of servitude.
Section 2 The Congress shall have the power to enforce this article by
appropriate legislation.
When Justice Scalia meant said that:
The Constitution explicitly protects racial minorities, that's what we
fought a civil war about, and the fourteenth amendment prevents /
forbids refusal to give equal protection of the laws in particular
with respect to race. So my Constitution protects that explicitly.
He is putting the equal protection clause of Section 1 of the 14th Amendment in the context of the rest of Section 1 of the 14th Amendment, which gave to former slaves citizenship (implicitly a race based change) that was fortified with provisions including the equal protection of the laws that they had been denied before it was adopted while all other adult men of those days had.
More broadly, he is discussing this in the larger context of the Civil War Amendments and in the context of the legislation that was enacted by Congress pursuant to the enforcement clauses of the 13th, 14th and 15th Amendments.
What these amendments do to protect racial minorities is to give them equal treatment when prior to their enactment they were given unequal treatment. Brown v. Board of Education which he discusses in the same breath, furthermore gives the 14th Amendment its modern meaning overruling Plessy v. Ferguson whose "separate but equal" interpretation of the equal protection clause of the 14th Amendment had facilitated the Jim Crow regimes of segregation in the South because after more than half a century it had become clear that separate was almost never actually equal in practice.
As a footnote, the 14th Amendment Privileges and Immunities clause in Section 1 of that amendment was intended to be the greater of the Section 1 protections, but was gutted early on by the Slaughterhouse Cases that interpreted it in a manner that made it virtually irrelevant, continues to be good law. There is no Brown v. Board of Education counterpart overruling the Slaughterhouse cases the way that Brown repealed Plessy.
Where is written in the 14th Amendment that race is a protected
minority?
The context and legislative history of the equal protection clause of the 14th Amendment, as enforced by contemporaneous enforcement legislation adopted by Congress, was clear to all in its meaning (even to textualist leaning originalists like Justice Scalia) that it first and foremost applied to the discrimination based upon race and former condition of servitude that the 15th Amendment called out explicitly.
The notion of a "protected minority" isn't a very clean or helpful way to think about what the 14th Amendment does, however. Instead, it prohibits de jure legal discrimination based upon race and upon other factors that have been determined to constitute impermissible means of making legal distinctions.
The notion of the 14th Amendment and anti-discrimination laws as conferring special treatment on "protected minorities" has not been the story of American civil rights law, unlike the case in Canada, for example, which uses a legal theory framework of vindicating and benefiting oppressed minorities, rather than less ambitiously, merely aiming for racial equality in the law. Justice Scalia's choice of words in the quoted material reflects the cultural lean of conservative politicians in the U.S. who have often tried to frame anti-discrimination law in this way, contrary to most (but not quite all) U.S. civil rights law legal theory (voting rights have more of a anti-oppression model, in part, due to the relevant Congressionally enacted enforcement legislation, especially the Voting Rights Act).
