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According to my computation, the 4x4x4 cube can be solved no more than 57 moves.
The solving algorithm is based on tsai's 8-step method which can be found here: link

The only modification is that I merged step 3 & step 4 to one step.

For some reasons, the algorithm cannot be defined to the conversions between subsets, but can be defined to the conversions between sets:

S0: <U R F D L B Uw Rw Fw Dw Lw Bw>
step 1 =>
S1: <U R F D L B> * <U R F D L B Uw2 Rw Fw2 Dw2 Lw Bw2>
step 2 =>
S2: <U R F D L B> * <U R2 F D L2 B Uw2 Rw2 Fw2 Dw2 Lw2 Bw2>
step 3 & step4 =>
S3: <U R F D L B>
3x3x3 solver =>
S4: Solved State