The generator matrix
1 0 0 0 0 1 1 1 0 1 1 X 1 0 0 1 X 1 0 1 1 X 0 1 1 0 1 0 1 1 0 1 X 1 1 1 1 1 1 0 1
0 1 0 0 0 0 0 0 0 1 1 1 1 1 X 1 1 X+1 1 X 0 X 1 X X 1 X+1 0 X+1 1 1 0 1 X 0 X 1 1 0 1 0
0 0 1 0 0 0 1 1 1 1 X+1 0 0 X+1 X 1 X X 1 0 X 1 X 1 0 1 X 1 X+1 X 0 X X+1 X 1 X 1 X 0 0 1
0 0 0 1 0 1 1 0 1 X X+1 1 0 1 0 X+1 X 1 0 1 X 1 0 1 X X 0 0 0 X+1 0 X+1 0 X 1 X 0 X+1 X+1 X 1
0 0 0 0 1 1 0 1 X+1 X X+1 X+1 1 X 1 1 X 0 X+1 1 X X+1 X X+1 X+1 0 X X+1 X+1 X+1 X+1 X 0 1 1 1 X 1 1 1 0
0 0 0 0 0 X 0 0 X 0 X X X X X 0 X X 0 0 X X 0 X X X X 0 X X X X X X X 0 X X X X 0
0 0 0 0 0 0 X 0 0 0 0 0 X 0 X X X 0 X 0 0 X X 0 X 0 X X 0 0 0 X X 0 X X X X X X X
0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X X X X X X X X 0 X X X X X X 0 0 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+250x^32+568x^34+920x^36+1056x^38+1298x^40+1252x^42+1200x^44+892x^46+481x^48+196x^50+72x^52+4x^54+1x^56+1x^72
The gray image is a linear code over GF(2) with n=82, k=13 and d=32.
This code was found by Heurico 1.16 in 5.08 seconds.