I came with an interesting idea to think of this 4D representation. I think of each small square as a floor in a building, and the column which contains it is the building itself, representing 3D space (so a 4x4x4 cube). So if you move inside a single column, that would be equivalent to a 3D sokoban game. But you can also teleport across columns to the same 3D coordinates (but different 4th coordinate).