The generator matrix

 1  0  0  1  1  1  0  1  1  1  1  0  0  1  0  X  0  1  X  1  0  1  X  1  1  1  0  X  1  1  1  1  X  0  X  0  1  1  1  X  1
 0  1  0  1  0  1  1  0  X  1  1  X  1  0  1  X  X  1  1  1  1 X+1  1  0  0  0  1  0  X  0 X+1  0  1  1  1  X  0  1  1  1  0
 0  0  1  1  1  0  1  X  1  0 X+1  1  0  1  1  1  1  X  0  1 X+1  X  X  0 X+1 X+1 X+1  1  0  0  X  1 X+1  1 X+1  1  1  X  X  1  0
 0  0  0  X  0  0  0  X  X  X  X  0  0  0  X  0  X  0  X  X  X  0  X  X  X  X  0  X  X  0  0  X  0  X  X  0  0  0  X  X  0
 0  0  0  0  X  0  0  0  X  0  X  X  X  0  X  0  X  X  X  X  0  X  0  0  X  X  0  0  0  X  0  0  X  X  0  X  X  X  X  X  0
 0  0  0  0  0  X  0  0  0  X  0  0  X  0  0  X  X  0  X  0  X  0  X  X  X  0  X  X  0  X  0  0  X  X  0  X  0  X  0  0  0
 0  0  0  0  0  0  X  X  X  X  X  X  X  X  X  0  0  X  0  0  X  0  0  0  0  0  X  0  0  X  X  0  0  0  0  X  X  X  X  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+25x^34+66x^35+74x^36+82x^37+104x^38+82x^39+73x^40+86x^41+76x^42+58x^43+62x^44+62x^45+30x^46+46x^47+37x^48+26x^49+19x^50+4x^51+8x^52+2x^54+1x^56

The gray image is a linear code over GF(2) with n=82, k=10 and d=34.
This code was found by Heurico 1.16 in 0.0882 seconds.