Breaking simple (non-cryptographic) hashes is usually a great use case for an SMT solver like Microsoft's Z3. Unfortunately the approach is mostly defeated by the mapping of the input buttons to a set of arbitrary constants, so it resorts to considering a large number of disjunct possibilities---basically a very fancy brute force.
Nonetheless, I took a stab at it and I was indeed able to find the solution TXTUDUTXTUDUTXTUDU -- but I had to cheat and tell it the code repeats 3 times.
https://gist.github.com/rgov/e2d8f6831288ca739d5c51b0c9f4005...