The generator matrix
1 0 0 0 1 1 1 1 X 1 1 X 1 1 0 X X 0 1 X 1 1 1 1 0 1 1 X 1 0 0 1 1 1 1 0 0 1 0 0
0 1 0 0 0 1 X 0 0 1 1 1 X+1 X 1 0 1 0 X 1 X+1 X X X+1 1 0 1 X 0 1 1 1 X 1 0 1 X 1 0 1
0 0 1 0 1 1 1 X 1 X 0 0 X+1 1 0 1 1 1 0 1 1 X 1 0 X X 1 X X X+1 X X X+1 X+1 X+1 X+1 1 X 1 1
0 0 0 1 1 0 0 1 1 X+1 X X+1 X+1 X X X X X+1 1 X X+1 0 1 0 X+1 X+1 1 1 X+1 X+1 X+1 X 1 0 0 0 X X X X+1
0 0 0 0 X 0 0 0 0 0 0 0 X X 0 0 X X X X X X 0 X 0 X 0 X X 0 X 0 0 X 0 X 0 X X X
0 0 0 0 0 X 0 0 0 0 0 0 X X X X X X 0 0 0 X X X X 0 0 X X 0 0 X X 0 X X 0 0 0 0
generates a code of length 40 over Z2[X]/(X^2) who´s minimum homogenous weight is 34.
Homogenous weight enumerator: w(x)=1x^0+97x^34+210x^36+191x^38+135x^40+122x^42+110x^44+84x^46+51x^48+17x^50+4x^52+1x^54+1x^56
The gray image is a linear code over GF(2) with n=80, k=10 and d=34.
This code was found by Heurico 1.16 in 0.111 seconds.