The 4x4 doesn't have a corresponding superflip state, because the definition of the superflip is ambiguous, and no good definition leads to a known superflip position.
If you define the superflip state as "all edges flipped," then it is possible to treat the edge pairs like 3x3 edges and the center four pieces as 3x3 centers. This will allow you to create a superflip orientation on the 3x3 reduction of the 4x4. This is not, however, a state requiring the maximum moves to solve on the 4x4, because the centers remain solved.
If you define the superflip state as a checkerboard going in from each edge (roughly speaking), then no even numbered cube has one. To see why, remember that the corners stay fixed on a regular superflip to preserve the cube's symmetry - this can't happen for even puzzles.
Imagine the red-blue edge. The first corner has red on top, then the next edge has blue, next edge red, and last corner is blue. The first corner has red atop it, and the second has blue, which means one was necessarily swapped with the corner on the opposite side of the cube. This makes the checkerboarding pattern not possible to complete in any sense without swapping corners.
Finally, if you define the superflip as "the position taking the longest number of moves to solve," it may be some variant of these positions, but it likely wouldn't be recognizable as a regular superflip. This position isn't known, though. The 3x3 superflip position was demonstrated to take the maximum number of moves when it was proved the 3x3 can be solved in 20 moves.
No such analysis has been done on the 4x4, which would be required to find and prove such a state needs the maximum moves.
(If I recall, though I can't seem to find a reference for this, on the 4x4, the estimate for optimum move sequence is 33.)