50 moves rule is totally inappropriate in 4D. Let us dismiss that rule here, yes.
An upper bound is 17 queens: 16 threaten all 6^4 inner squares, then the 17th moves to the inner square closest to the king.
Edit: Nevermind, this amounts to the 17th queen checkmating the king on a 3D board with warp sides.
50 moves rule is totally inappropriate in 4D. Let us dismiss that rule here, yes.
An upper bound is 17 queens: 16 threaten all 6^4 inner squares, then the 17th moves to the inner square closest to the king.
Edit: Nevermind, this amounts to the 17th queen checkmating the king on a 3D board with warp sides.