The generator matrix

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

generates a code of length 50 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+28x^49+82x^50+6x^52+4x^54+1x^56+4x^57+2x^58

The gray image is a code over GF(2) with n=400, k=7 and d=196.
This code was found by Heurico 1.16 in 0.047 seconds.