The generator matrix

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

generates a code of length 41 over Z2[X]/(X^2) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+34x^32+110x^33+160x^34+196x^35+262x^36+274x^37+295x^38+286x^39+258x^40+300x^41+309x^42+338x^43+320x^44+256x^45+231x^46+178x^47+93x^48+78x^49+58x^50+26x^51+22x^52+6x^53+2x^54+2x^56+1x^66

The gray image is a linear code over GF(2) with n=82, k=12 and d=32.
This code was found by Heurico 1.10 in 0.437 seconds.