Use an ultra magic 13x13 square to construct a 13x13x13x13 magic cube. Construct the first grid by placing the 13x13 magic square in the middle level of the middle (3D-)cube. Create by shift-2 in the rows and columns 169 different shifted versions of the 13x13 magic square, filling the 13x13x13x13 magic cube. Construct the second grid by using shift-2 in the opposite direction.
The 13x13x13x13 magic cube is pantriagonal & panquadragonal magic, panmagic in the levels and 1/2 pandiagonal magic through the levels. So the 13x13x13x13 magic cube misses 1/2 magic feature to be Nasik perfect. The smallest four dimensional Nasik perfect magic cube is the 16x16x16x16 magic cube.
See for grids, the result and the check (if all numbers are in the magic cube and addition of the numbers give the right magic sum) the download below.