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 X 1 1 X 1 1 1 1 X 1 X 1 1 X 1 1 1 1 X 1 1 1 0 1 0 1 1 1 1 1 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 X 0 X X X X 0 X X X X X 0 0 0 0 0 X 0 X X 0 X 0 X 0 0 0 0
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 X X 0 0 X 0 0 X X X 0 0 0 0 0 X 0 0 X 0 X 0 0 X X 0 0 X 0 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 X 0 0 X X 0 0 X 0 0 0 X X X X X X X X 0 0 0 0 X 0 0 0 X 0 0 X
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 X 0 0 X X 0 X 0 X X X 0 X 0 0 X 0 0 0 X 0 X 0 X 0 0 0 X X 0 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 0 X 0 X 0 0 0 0 X 0 0 0 X X X X 0 0 X X X 0 X X 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 0 X X X X 0 0 X X 0 X 0 0 0 X 0 0 0 0 0 X X X 0 0 0 0 0 X X 0
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 X X 0 0 0 X X X 0 0 0 X X 0 0 X 0 0 X X X X X X X X 0 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 X X X X 0 X X 0 X 0 X 0 0 0 X 0 X 0 X X X X X X X 0 0 X 0 X
generates a code of length 72 over Z2[X]/(X^2) who´s minimum homogenous weight is 64.
Homogenous weight enumerator: w(x)=1x^0+194x^64+128x^68+404x^72+128x^76+140x^80+28x^88+1x^128
The gray image is a linear code over GF(2) with n=144, k=10 and d=64.
This code was found by Heurico 1.16 in 45.6 seconds.