The generator matrix

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

generates a code of length 41 over Z2[X]/(X^2) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+137x^34+317x^36+341x^38+269x^40+287x^42+263x^44+228x^46+122x^48+59x^50+20x^52+3x^54+1x^58

The gray image is a linear code over GF(2) with n=82, k=11 and d=34.
This code was found by Heurico 1.10 in 0.125 seconds.