I'm assuming you live in the US.
"By definition, copyright is the protection of the works of artists and authors giving them the exclusive right to publish their works or determine who may so publish" (Steven H. Gifis).
It doesn't matter if you have the intention to make money using that material. The degree of unauthorized use which constitutes infringement is open to debate, though. Copying substantial parts of copyrighted material is crossing the line, but there is a certain amount of freedom.
To put it in terms of cartoons, think of the amount of stories taken from novels, plays, movies, etc. Also, there are plenty of instances where a a character, plot line or catchphrase from one show is parodied, used or copied on another (as an example, the two part South Park episode making continued use of Family Guy characters seemed to be in the clear).
I reckon a small homage or reference is fine: if you only intend to use it for a few signs in the background of a home made game, there shouldn't be any problems (although if you actually want to publish it on a large scale you might want to run it by the Fox legal department, just to be sure).
For more information, see the Copyright Act of 1976 (since then pretty much all copyright is protected by federal statute). There's a heap of jurisprudence on this subject, so if you feel like reading up on copyright law, there's enough literature out there to keep you occupied for the next few years