The generator matrix

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

generates a code of length 50 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+270x^48+512x^50+224x^52+16x^56+1x^96

The gray image is a code over GF(2) with n=400, k=10 and d=192.
This code was found by Heurico 1.16 in 0.672 seconds.