The generator matrix

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

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+188x^40+494x^42+805x^44+936x^46+1087x^48+1200x^50+1070x^52+996x^54+745x^56+418x^58+189x^60+52x^62+10x^64+1x^88

The gray image is a linear code over GF(2) with n=100, k=13 and d=40.
This code was found by Heurico 1.10 in 2.17 seconds.