The generator matrix

 1  0  0  0  1  1  1  0  1  1  1  1  X  X  X  1  X  0  0  1  1  0  X  0  X  1  1  1  1  1  1  X  1  1  1  1  X  0  1  X  1
 0  1  0  0  0  1  1  1  X  0 X+1 X+1  1  1  X X+1  1  1  0 X+1  0  X  1  1  0 X+1 X+1  1  0  1 X+1  1  1  1 X+1  0  1  1  X  1  0
 0  0  1  0  1  1  0  1  0 X+1 X+1  X  X X+1  1  0 X+1  1  1  1 X+1  0  0 X+1  1  1 X+1  0  X X+1  0 X+1  X  0 X+1  X X+1  X X+1  0  1
 0  0  0  1  1  0  1  1  1  0  1  X X+1  0  1  X X+1  0  X  0  1  1  X  1  1 X+1  X  X  X  1 X+1  0 X+1  1  0  0 X+1  1 X+1  1  1
 0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  X  X  0  X  0  X  X  0  X  0  0  X  X  X  0
 0  0  0  0  0  X  0  0  0  0  0  0  X  0  X  X  0  X  X  0  0  X  X  0  X  X  0  X  X  X  X  X  0  X  X  0  X  0  0  0  0
 0  0  0  0  0  0  X  0  0  0  0  0  0  X  X  0  X  X  X  X  X  0  X  0  X  0  0  0  0  X  X  0  X  X  0  X  X  X  0  X  0
 0  0  0  0  0  0  0  X  X  X  0  X  X  X  X  X  0  0  0  0  X  X  0  0  X  0  0  0  X  X  0  0  0  X  0  X  0  0  X  0  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+51x^32+84x^33+152x^34+222x^35+247x^36+272x^37+298x^38+268x^39+295x^40+308x^41+297x^42+360x^43+271x^44+284x^45+216x^46+148x^47+138x^48+72x^49+54x^50+26x^51+17x^52+4x^53+6x^54+3x^56+1x^58+1x^60

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 1.21 seconds.