"I don't recall signing anything when I got hired stating that I won't
be messing with the system."
The first thing to do is read your employee handbook and work contract. Chances are very good that your activities are against company policies - which can be widely defined as bypassing any part of the company network by known or unknown means to reach any other network that is off limits during work and while using the company facilities - and those documents will outline what legal actions the company can take against you. Like fire you.
Laws do vary from state to state, but employers have wide leeway in hiring and firing. Even if what you have done isn't explicitly against company policies, they can fire you for wearing a red shirt one day.
Or is it the filter-team to blame that they didn't do a very good job
Someone leaving a door unlocked doesn't give you the legal right to walk into their house. Sure, they could be "blamed", but that's for the company to decide and action against them, and it is not a legal defense for your actions.
The company defines what hacking might be defined as on their network by their contract with you. But specifically writing code is a specific action taken to arrive at the result of bypassing the filter, and is not accidental. That's "messing with the system" which you can be very reasonably sure is not allowed under your work contract.