The generator matrix

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

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+48x^50+10x^52+5x^56

The gray image is a code over GF(2) with n=400, k=6 and d=200.
This code was found by Heurico 1.16 in 0.062 seconds.