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 X 1 1 1 1 1 X 1 1 1 1 1 1 1 X 1 1 1 1 X 1 1 1 X 1 1 0 1 X 1 X 1 1 1 X 1 X X X
0 X 0 0 0 0 0 0 0 0 X 0 0 0 X X 0 0 0 0 X X X X 0 X X 0 X X 0 X 0 0 0 X 0 0 X X 0 0 X 0 X X 0 X 0 X X 0 X 0 X 0 0 X X 0 X X 0 0 0 0 0 X X 0 X X X 0 X 0 0 0 0 X X 0
0 0 X 0 0 0 0 0 0 0 X X X X X X X X X X X X X X 0 X 0 0 X 0 X 0 0 0 X X 0 X X 0 X X X X X X X 0 X X 0 X 0 0 0 0 0 0 0 0 X X X X X 0 0 X X 0 0 0 X 0 0 0 X X 0 0 0 0
0 0 0 X 0 0 0 0 0 X 0 X X X 0 0 X X X 0 0 X X X 0 X 0 X 0 0 0 X 0 X X 0 0 X 0 0 X 0 0 0 0 X 0 0 X X 0 X X 0 X 0 X 0 0 X X X 0 X 0 X X X 0 X X X X 0 X X X X 0 X X 0
0 0 0 0 X 0 0 0 0 X 0 0 0 X 0 X X 0 X X X X X X 0 X 0 X X X 0 0 X 0 0 0 X X 0 0 0 0 X X X 0 0 X X 0 0 X 0 0 0 0 X 0 X X 0 X 0 0 X X 0 X 0 X 0 X X X 0 0 X 0 X 0 X 0
0 0 0 0 0 X 0 0 0 X 0 0 X X X X 0 X 0 X 0 0 0 X 0 X X X X X X X 0 0 X X X X 0 0 0 0 X 0 0 X 0 0 X 0 0 0 X X X X 0 0 0 0 0 0 0 X X X 0 0 X 0 0 X X X X 0 X X X X 0 X
0 0 0 0 0 0 X 0 0 X 0 X X 0 X 0 X 0 0 X X 0 X X 0 0 X X X 0 0 0 X X X 0 X 0 X 0 0 0 0 0 X X X 0 X X 0 0 X X 0 0 X X X X 0 0 X 0 X 0 X X X 0 0 0 X X 0 X X 0 0 X 0 X
0 0 0 0 0 0 0 X 0 X X X 0 0 0 X X X 0 X 0 0 X X X X X 0 0 X 0 0 0 0 X 0 X 0 0 X X X X 0 X 0 0 X 0 X X X 0 0 X X 0 0 0 0 0 0 0 X 0 0 X 0 X X X 0 X 0 X 0 X X X 0 X 0
0 0 0 0 0 0 0 0 X X X 0 X 0 0 0 0 X X X X 0 0 X X 0 0 0 X X 0 X 0 0 0 0 0 X X 0 X 0 X 0 X 0 X 0 X X X 0 0 X X 0 X X 0 0 0 X 0 0 0 0 X X 0 X X X 0 X 0 X X 0 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+80x^72+8x^74+157x^76+56x^78+182x^80+120x^82+155x^84+72x^86+92x^88+49x^92+41x^96+5x^100+4x^104+1x^108+1x^140
The gray image is a linear code over GF(2) with n=164, k=10 and d=72.
This code was found by Heurico 1.16 in 0.419 seconds.