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

generates a code of length 59 over Z2[X]/(X^3) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+40x^50+64x^51+131x^52+156x^53+217x^54+240x^55+274x^56+342x^57+389x^58+466x^59+388x^60+382x^61+284x^62+178x^63+153x^64+114x^65+58x^66+70x^67+57x^68+30x^69+27x^70+6x^71+20x^72+8x^74+1x^90

The gray image is a linear code over GF(2) with n=236, k=12 and d=100.
This code was found by Heurico 1.16 in 1.13 seconds.