The generator matrix

1 0 0 0 0 0 1 1 1 X 1 1 0 1 1 0 X 1 1 1 X 0 1 1 X 0 1 1 0 X X 0 0 0 0 X X 1 0 0 0
0 1 0 0 0 0 0 0 0 0 0 0 0 X X X X 1 X+1 1 1 1 X+1 X+1 1 1 0 0 X X 1 1 1 1 1 X 1 1 1 0 0
0 0 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 X+1 X+1 0 X+1 1 X+1 X X X+1 X 1 X 1 X X X+1 1 1 0 1 0 X+1 1 0
0 0 0 1 0 0 0 1 1 1 0 X X 1 X+1 X+1 1 1 X X 0 X+1 0 X+1 X+1 X 0 X+1 0 X X 1 1 1 1 1 X 0 X X+1 1
0 0 0 0 1 0 1 0 X+1 1 1 0 X+1 0 X+1 1 X 1 X 1 X+1 X 1 X+1 X 0 X+1 X 1 0 1 X X+1 0 X 1 X+1 X+1 0 0 X
0 0 0 0 0 1 1 X+1 X 1 X 1 1 0 X+1 0 1 0 0 X 0 X X+1 X+1 1 1 1 0 X X X+1 X+1 0 0 X+1 X 1 X+1 X 0 X
0 0 0 0 0 0 X X 0 0 0 0 X 0 0 0 X 0 0 0 0 0 X X 0 0 0 X X X X X X X 0 X 0 X X X 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+226x^32+625x^34+871x^36+1065x^38+1317x^40+1288x^42+1119x^44+907x^46+500x^48+202x^50+61x^52+8x^54+1x^58+1x^68

The gray image is a linear code over GF(2) with n=82, k=13 and d=32.
This code was found by Heurico 1.10 in 1.78 seconds.