I would like to know if the Great Seal (with modified text, see here https://i.stack.imgur.com/Mwo6K.jpg) could be used as in a non-commercial way that doesn't go against the law.
There is actually a law against using the Great Seal. 18 U.S. Code § 713 says:
(a) Whoever knowingly displays any printed or other likeness of the great seal of the United States, or of the seals of the President or the Vice President of the United States, or the seal of the United States Senate, or the seal of the United States House of Representatives, or the seal of the United States Congress, or any facsimile thereof, in, or in connection with, any advertisement, poster, circular, book, pamphlet, or other publication, public meeting, play, motion picture, telecast, or other production, or on any building, monument, or stationery, for the purpose of conveying, or in a manner reasonably calculated to convey, a false impression of sponsorship or approval by the Government of the United States or by any department, agency, or instrumentality thereof, shall be fined under this title or imprisoned not more than six months, or both.
(e) Whoever, except as directed by the United States Congress, or the Secretary of the Senate and the Clerk of the House of Representatives, acting jointly on its behalf, knowingly uses, manufactures, reproduces, sells or purchases for resale, either separately or appended to any article manufactured or sold, any likeness of the seal of the United States Congress, or any substantial part thereof, except for manufacture or sale of the article for the official use of the Government of the United States, shall be fined under this title or imprisoned not more than six months, or both.
I am not sure if someone could make a First Amendment argument, but it seems likely. I note that Wikipedia isn't afraid to have pictures of the Great Seal on the webpage about it. Also, a modified Great Seal was used in the film National Treasure: Book of Secrets (although it purported to be a presidential seal). I also found an instance where the White House officially asked the Onion to stop using the Presidential seal, but it's unclear what happened with that. The Onion did not immediately remove the seal, however, and I think we would have heard if they had been arrested. I do not believe that Wikipedia, the filmmakers, and the Onion would have done this if there was a serious risk of six months in prison. In each of those cases, there was a strong First Amendment speech/press use, and there was no risk of anyone thinking the seal was being used for a government endorsement.
There is an executive order (visible from the "Notes" section of the link to the law) regarding the use of the seals of the President and Vice President:
Section 1. Except as otherwise provided by law, the knowing manufacture, reproduction, sale, or purchase for resale of the Seals or Coats of Arms of the President or the Vice President of the United States, or any likeness or substantial part thereof, shall be permitted only for the following uses:
(a) Use by the President or Vice President of the United States;
(b) Use in encyclopedias, dictionaries, books, journals, pamphlets, periodicals, or magazines incident to a description or history of seals, coats of arms, heraldry, or the Presidency or Vice Presidency;
(c) Use in libraries, museums, or educational facilities incident to descriptions or exhibits relating to seals, coats of arms, heraldry, or the Presidency or Vice Presidency;
(d) Use as an architectural embellishment in libraries, museums, or archives established to house the papers or effects of former Presidents or Vice Presidents;
(e) Use on a monument to a former President or Vice President;
(f) Use by way of photographic or electronic visual reproduction in pictures, moving pictures, or telecasts of bona fide news content;
(g) Such other uses for exceptional historical, educational, or newsworthy purposes as may be authorized in writing by the Counsel to the President.
This provides several legal ways to use the Presidential seals. However, the seal of the President is not the same as the Great Seal, so this technically does not apply if you want to use the Great Seal in particular.
The "real, original" Great Seal is a US government work created in 1782, and is not protected by copyright. There have been a number of derivative works based on that created since then. There may be some contemporary version which is (in part) protected by copyright, in which case you would have to contact the copyright holder.