The point is that the police can't prove you do or do not remember a code. Consequently, they can't compel you to use that code.
However, since your thumbprint definitely exists, they can compel you to use it.
As I understood it, the police can not compel you to tell them something you know because this would be analogous to testifying against yourself, however, they can require you to give them something you have (or something they would find with a warrant) because it is a physical thing, not testimony.
It's the difference between being required to give up a safe combination which the police can not compel you to tell them, vs, a key to a safe which the police could search you for and take from you and use to open the safe within the bounds of a warrant (or some other theoretical circumstances).
Also, they can't coerce you to reveal the code even if they can prove you know it. Confessions extracted under torture by inquisitors was a recent memory when the Bill of Rights was drafted.