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

generates a code of length 58 over Z2[X]/(X^3) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+139x^50+8x^51+273x^52+72x^53+401x^54+160x^55+522x^56+256x^57+570x^58+296x^59+423x^60+168x^61+328x^62+48x^63+173x^64+16x^65+137x^66+71x^68+23x^70+7x^72+2x^74+1x^76+1x^88

The gray image is a linear code over GF(2) with n=232, k=12 and d=100.
This code was found by Heurico 1.16 in 1.16 seconds.