The generator matrix

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

generates a code of length 50 over Z2[X]/(X^2) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+38x^40+82x^41+121x^42+154x^43+233x^44+228x^45+261x^46+268x^47+267x^48+286x^49+248x^50+298x^51+256x^52+298x^53+252x^54+230x^55+178x^56+104x^57+115x^58+68x^59+47x^60+26x^61+23x^62+6x^63+4x^64+4x^66

The gray image is a linear code over GF(2) with n=100, k=12 and d=40.
This code was found by Heurico 1.16 in 1.6 seconds.