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 1 1 1 1 1 1 X X 1 1 1 1 1 1 1 1 1 1 1 X 1 1 1 X X 1 X X 0 1 1 X 1
0 X 0 0 0 0 0 0 0 0 X 0 X X 0 X 0 0 X 0 X X 0 0 X 0 X 0 0 X X X X 0 X 0 0 X 0 X 0 0 0 0 X X X 0 0 X 0 X 0 X X 0 0 0 X X 0 X 0 0 0 X X 0 X X 0 X 0 0 X 0 0 0 X X X
0 0 X 0 0 0 0 0 0 0 X X X 0 X X 0 0 0 0 X X 0 X 0 X X X X X X 0 0 0 X 0 X 0 0 0 X X 0 0 X 0 0 0 X 0 0 X 0 0 X X 0 X 0 X 0 X X 0 0 X 0 X X 0 X 0 X 0 X X X X X X X
0 0 0 X 0 0 0 0 0 X 0 X 0 X X 0 0 X 0 0 X X 0 0 X X 0 0 0 X X 0 X X 0 X 0 X 0 X 0 0 X X 0 0 0 X 0 X 0 0 X 0 X 0 X 0 0 X X X X X X X 0 0 X 0 0 0 0 X 0 X X 0 0 X 0
0 0 0 0 X 0 0 0 0 X 0 0 0 0 X X 0 X X 0 X X X 0 0 0 X X 0 0 X 0 X X X 0 0 0 X X X 0 0 X X 0 X 0 0 0 0 0 X X 0 X X X X X 0 0 0 0 0 X 0 X 0 X 0 0 X 0 X X 0 X 0 X 0
0 0 0 0 0 X 0 0 0 X 0 0 X X X X 0 0 0 X 0 X X X X X X 0 X 0 X 0 X 0 0 0 X 0 X X 0 X 0 X X X X X X 0 X X 0 X 0 X 0 X X 0 X X X X X 0 0 0 X 0 0 X 0 0 X 0 0 X X X X
0 0 0 0 0 0 X 0 0 X 0 X X 0 0 0 X 0 X 0 X X 0 0 0 X X 0 X 0 X X X X 0 0 X X 0 X X X X X X X 0 X 0 X X X X X 0 X X 0 X 0 0 X X X 0 X X X 0 X 0 0 0 0 0 0 X X 0 X X
0 0 0 0 0 0 0 X 0 X X X 0 0 0 X 0 0 X X 0 X 0 X X X 0 X 0 0 0 0 0 X 0 X X X X 0 0 X X 0 0 X 0 X 0 X 0 X X 0 X 0 0 X X 0 X X 0 0 0 0 X X 0 X X X 0 X X X 0 X X X 0
0 0 0 0 0 0 0 0 X X X 0 0 X 0 0 X X X 0 X 0 X X X 0 0 0 X 0 X X X 0 0 0 0 0 0 0 X X 0 X X 0 X 0 X X X X X X X 0 0 0 0 0 X X 0 X X 0 X 0 0 0 0 X 0 X 0 0 X 0 0 X 0
generates a code of length 81 over Z2[X]/(X^2) who´s minimum homogenous weight is 72.
Homogenous weight enumerator: w(x)=1x^0+173x^72+80x^76+384x^80+176x^84+165x^88+42x^96+2x^104+1x^144
The gray image is a linear code over GF(2) with n=162, k=10 and d=72.
This code was found by Heurico 1.16 in 7.49 seconds.