The generator matrix
1 0 0 1 1 1 0 1 1 1 1 1 0 X 0 1 0 1 1 0 1 1 0 X X X 1 0 1 1 0 1 X X 1 0 1 X 1 1 X
0 1 0 1 0 1 1 0 0 1 X+1 X 1 1 0 X 0 X+1 X 1 X+1 X+1 1 X 1 1 0 1 1 0 1 X 1 X 1 X 0 1 1 0 0
0 0 1 1 1 0 1 0 1 X+1 X 1 X 1 1 0 1 X+1 X X 0 0 0 1 X 1 0 X+1 0 X 0 X+1 X+1 1 X 1 X+1 1 X 0 X
0 0 0 X 0 0 0 0 0 X 0 0 0 0 0 0 0 X 0 X X X X X 0 X X 0 0 0 0 X 0 X 0 X X 0 X 0 X
0 0 0 0 X 0 0 0 0 0 0 0 X X X X 0 X 0 0 X 0 X X X 0 0 0 0 X X 0 X 0 0 0 X X 0 X 0
0 0 0 0 0 X 0 0 0 0 X 0 0 0 0 0 0 0 0 0 X X X X X X X 0 X X X 0 0 0 X X 0 X X X X
0 0 0 0 0 0 X 0 0 0 0 0 0 X 0 0 X X X X X 0 0 0 X X 0 X X X X X 0 0 0 X 0 X 0 0 0
0 0 0 0 0 0 0 X 0 X X X 0 0 X 0 X X X 0 X 0 X 0 X 0 X 0 0 0 X X 0 X X X 0 0 X 0 0
0 0 0 0 0 0 0 0 X 0 0 X X X X X 0 X 0 X 0 X 0 0 X X 0 X 0 0 0 X X 0 X 0 0 0 0 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+147x^32+212x^34+519x^36+520x^38+692x^40+584x^42+611x^44+400x^46+288x^48+68x^50+37x^52+8x^54+8x^56+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 1.36 seconds.