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

generates a code of length 58 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+62x^50+131x^52+32x^53+119x^54+160x^55+130x^56+320x^57+165x^58+320x^59+130x^60+160x^61+109x^62+32x^63+104x^64+42x^66+9x^68+11x^70+4x^72+3x^74+2x^76+1x^78+1x^96

The gray image is a code over GF(2) with n=232, k=11 and d=100.
This code was found by Heurico 1.16 in 0.523 seconds.