I think the main premise of the film doesn't make any sense unless it's somehow explained in some other film. I mean although it's seen that the one who puts the code on Fry is

Bender, when he travels back in time to Lars's funeral.

The code could only be put because

the code already existed in Lars. It looks like the only reason that Bender could put the code on Fry is because it already existed on Fry. No one somehow obtained the knowledge to create the code. This creates a circular paradox which would make all the events impossible to happen.

Am I missing something?