The generator matrix

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

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+42x^32+86x^33+133x^34+226x^35+282x^36+270x^37+288x^38+304x^39+306x^40+304x^41+274x^42+308x^43+296x^44+256x^45+206x^46+160x^47+147x^48+106x^49+56x^50+26x^51+14x^52+2x^53+2x^54+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 1.16 in 1.16 seconds.