The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  0  X  2  X 2X  X 2X+2  1  1  1  1  1  1  X  X  X  X  1  1  X  X  X  X  0 2X  2 2X+2 2X+2 2X+2  0 2X  1  1
 0  X  2 3X+2 2X X+2 2X+2 3X  0 3X+2  2 3X 2X X+2 2X+2  X 3X+2  X 3X  X X+2  X  X  X  0  2 2X 2X+2 3X+2 3X  2  0 2X 2X+2 X+2  X 3X+2 X+2 3X  X  X  X  X  X  2 2X+2 2X+2 2X+2  0 2X

generates a code of length 50 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+116x^50+3x^52+4x^54+3x^56+1x^60

The gray image is a code over GF(2) with n=400, k=7 and d=200.
This code was found by Heurico 1.16 in 0.062 seconds.