Yes, you can indeed customise it from a standard cube, but it's really a pretty forgettable puzzle. Believe it or not, any state on the puzzle can be solved with at most 2 turns (3 if you only count quarter turns). Hendrik Haak has a picture of this puzzle which was modified from a Professor's Cube (why anyone would want to destroy a perfectly good Professor's Cube in this way is beyond me) at http://www.puzzle-shop.de
(select "Museum" --> "2x2 Special"). If you'd really like to make one anyway (as a conversation piece, perhaps), it's basically set up like an offset 2x2x2 puzzle, so you'd have a 1x1x1 block, 3 1x1x2 blocks, 3 1x2x2 blocks, and a 2x2x2 block. The 1x1x1 and 2x2x2 blocks are on diametrically opposite corners, the 1x1x2 blocks are lined up against the 1x1x1 block like on the Bandaged Cube, and the 1x2x2 blocks fill in the gaps against the 2x2x2 block. L8r.