IF Russia had the "nuclear codes" whatever that means (is it launch codes maybe) they would do them no good at all.
The missiles don't get launched just because the codes get published on the front page of the NY Times. The code has to be transmitted to the launch command post over a secure line. You don't mail it to them, call them on their cell phone, or even call on an ordinary phone line. It has to come in on a very, very secure line which does not have an extension in Russia.
The secure line from the football. Not mention that the missiles would be launched at Russian.