whats a sheet of ply worth there?
4 sheets of 8x4 ply can make a 4x4x6 box. 1/4" ply should be ok.
3 4x6 for back and sides, the 3 2x4 offcuts make the front/door and the 4th sheet cut in half makes the top and bottom.
some 1" sq in the corners, about 60 screws, 4 hinges, some liquid nails, a...