The generator matrix
1 0 1 1 1 0 1 1 0 1 1 X 1 1 0 1 0 1 1 X 1 1 0 1 1 0 1 1 1 0 X 1 1 0 0 1 1 1 1 X 1 1 1 1 X 0 1 1 1 1 1 0 1 1 1 1 X 1 1 0 1 1 0 1 1 1 1 1 1 1 0 1 1 X 1 0 1 1 1 1 1 X
0 1 1 0 1 1 0 1 1 X X+1 1 0 X+1 1 X+1 1 0 X+1 1 0 X 1 X+1 X 1 X+1 X+1 0 1 1 1 X+1 1 1 0 X X+1 X+1 1 X+1 0 X X+1 1 1 0 1 X X 0 1 X 0 X 1 1 0 0 1 1 X 1 0 X+1 1 1 X X 0 1 X X+1 1 1 1 X+1 0 X 1 X+1 0
0 0 X 0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 X X 0 0 X 0 X X X X X 0 0 X X X X X X X X 0 X X X X 0 0 X X X 0 X X 0 X 0 X 0 0 X X 0 0 X X 0 X 0 0 0 0 0 0 0 0 X 0 0 X X X
0 0 0 X 0 0 0 0 0 X 0 0 0 0 0 X X 0 X X 0 0 X 0 X 0 X 0 X X 0 X 0 X 0 X X 0 0 X 0 X 0 0 0 X X X 0 X X 0 0 X 0 X 0 X X 0 X 0 0 X X X X X X 0 X 0 0 X X X X X X 0 X X
0 0 0 0 X 0 0 0 0 0 X 0 0 X X X X X X 0 X 0 X X X 0 0 0 0 0 X 0 0 X X 0 0 0 0 X 0 0 0 X X X X 0 X 0 X X X 0 0 X X 0 X 0 X X 0 0 X 0 0 X X X 0 X 0 X 0 X X X X X X X
0 0 0 0 0 X 0 0 0 0 0 X 0 X X X 0 0 0 X X X X 0 X 0 X 0 X 0 X X X 0 X 0 0 X X 0 X X 0 0 X X 0 X 0 X X X 0 X 0 0 0 X X X X X X X X 0 0 0 X 0 X X 0 0 0 X X 0 0 0 X X
0 0 0 0 0 0 X 0 0 X 0 0 X X 0 X 0 0 0 0 X X X X 0 X 0 0 0 X 0 X 0 0 X X X 0 0 X X X X 0 X X 0 0 0 0 X X X 0 X 0 0 X X 0 X X 0 0 X X 0 0 0 0 X 0 X X 0 X 0 X X 0 X 0
0 0 0 0 0 0 0 X 0 0 X 0 X 0 0 X 0 X X 0 X 0 X X 0 X 0 X X 0 X X X 0 X X 0 0 X 0 X 0 0 0 X X 0 X X X 0 0 X 0 X 0 X X 0 X 0 0 X 0 X X 0 X X X X 0 0 X X 0 0 0 0 X X 0
0 0 0 0 0 0 0 0 X 0 0 X 0 X 0 0 X X X 0 X 0 X 0 X X 0 X 0 X X X 0 X 0 0 0 X 0 X X X X 0 X 0 0 X X X X X 0 X X 0 0 0 0 0 X 0 X 0 X 0 X 0 0 0 0 X X X X 0 0 X 0 0 0 X
generates a code of length 82 over Z2[X]/(X^2) who´s minimum homogenous weight is 72.
Homogenous weight enumerator: w(x)=1x^0+113x^72+122x^74+276x^76+184x^78+281x^80+196x^82+249x^84+176x^86+207x^88+82x^90+94x^92+8x^94+30x^96+18x^100+8x^104+2x^108+1x^116
The gray image is a linear code over GF(2) with n=164, k=11 and d=72.
This code was found by Heurico 1.16 in 1.07 seconds.