The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X X X X X X X 1 X X 1 0 X 0 1 1 0 1 0 1 1 1 1 X 0 X 1 1 1 1 1 X
0 X 0 0 0 0 0 0 0 0 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 X 0 X 0 0 0 X X X 0 X X X 0 0 X 0 X X 0 0 X 0 X X 0 X 0 0 0 X X X X 0 X X X X X 0 0 0 X 0 0
0 0 X 0 0 0 0 0 0 0 0 0 0 0 X 0 0 0 0 X X X X X X X 0 0 0 X 0 0 0 X X X 0 0 0 X X X 0 X X 0 0 X X X X 0 0 0 0 0 X 0 0 0 X 0 X X X 0 0 X 0 0 X X X X 0 0 X 0 X 0 0
0 0 0 X 0 0 0 0 0 0 0 0 0 X 0 0 0 X X X X X X 0 0 0 0 X 0 X X X 0 X 0 0 X X 0 0 0 X X X 0 X 0 X X 0 X X X 0 X X X 0 X 0 0 0 X 0 X 0 X 0 0 X 0 0 X 0 0 0 0 X 0 0 0
0 0 0 0 X 0 0 0 0 0 0 0 0 X 0 X X X X X X 0 X X 0 X X X 0 0 0 X X X X X 0 X X 0 0 0 X 0 0 0 0 X 0 0 0 0 0 X X 0 X 0 0 0 0 0 0 X 0 X X X 0 X X X X 0 X X X 0 0 X 0
0 0 0 0 0 X 0 0 0 0 0 0 X 0 0 X X 0 X X 0 X 0 X 0 X X X X 0 0 X X 0 0 0 X 0 X 0 0 0 0 X X 0 X X X X X 0 0 0 0 X 0 X 0 X X 0 0 X 0 0 0 0 0 X X X X X 0 X X X X X X
0 0 0 0 0 0 X 0 0 0 0 0 X 0 0 0 X X X X 0 X X 0 X 0 X 0 0 X 0 0 X X X 0 0 0 0 X 0 0 0 X X X X 0 X 0 0 0 X 0 X X 0 0 X 0 0 0 X X 0 X 0 0 X X 0 X X 0 X 0 X 0 0 0 X
0 0 0 0 0 0 0 X 0 0 0 X 0 0 0 0 X X 0 X 0 0 0 X X X 0 0 X 0 X X X X 0 0 0 X X X X X 0 0 0 0 X X X X X 0 X X 0 X X 0 X 0 X 0 X X 0 X X X 0 X 0 X 0 X 0 X 0 X X 0 X
0 0 0 0 0 0 0 0 X 0 0 X 0 0 0 X 0 0 X 0 X 0 0 X 0 0 0 0 X X X 0 0 X X 0 X X X X 0 0 0 X X X X 0 X 0 X X X X X X X X X X 0 X X X 0 0 0 X 0 X 0 X X X X 0 0 X X X 0
0 0 0 0 0 0 0 0 0 X 0 X X X X X 0 0 0 X 0 0 X X 0 0 X 0 X X 0 0 X X 0 X X 0 0 0 0 X 0 0 0 X 0 X 0 X X X 0 0 X 0 0 0 X 0 0 X X 0 X 0 X 0 X 0 0 0 X X X X X X 0 X 0
0 0 0 0 0 0 0 0 0 0 X X X X X 0 0 X X X X X 0 X 0 X 0 0 0 0 0 X 0 X 0 0 X 0 X X 0 0 0 X 0 0 X 0 0 X 0 0 X X X 0 X X X 0 X X 0 0 X X X 0 X X 0 X X 0 X X X 0 X X 0
generates a code of length 81 over Z2[X]/(X^2) who´s minimum homogenous weight is 66.
Homogenous weight enumerator: w(x)=1x^0+52x^66+109x^68+145x^70+199x^72+272x^74+364x^76+428x^78+528x^80+535x^82+400x^84+317x^86+251x^88+176x^90+112x^92+74x^94+53x^96+35x^98+21x^100+12x^102+8x^104+2x^106+1x^108+1x^124
The gray image is a linear code over GF(2) with n=162, k=12 and d=66.
This code was found by Heurico 1.16 in 5.69 seconds.