IANAL, but as a green card holder my lawyer told me they cannot deny you entry without an order from an immigration judge (likely if travel was not brief - more than 180 days, or they engaged in illegal activity after leaving the United States as defined in 8 U.S.C. 1101(a)(13)) - you only have to answer questions about your name and status, nothing more - though, obviously it will likely cause delays.
Still, give them the code if you want.