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 1 1 1 1 1 X 1 1 1 1 1 1 1 X 1 X 1 1 1 1 X 1 1 1 X 1 1 X 1 0 1 1 1 X X
0 X 0 0 0 0 0 0 0 0 X 0 X X 0 X 0 0 X 0 X 0 0 X 0 X X X 0 0 X 0 X X 0 X 0 X X X 0 0 0 0 0 X X 0 0 X X X X X 0 X X 0 X X 0 0 X 0 0 X 0 X 0 X 0 0 0 0 0 X 0 X X X 0 0 X 0 0 0 0 X X
0 0 X 0 0 0 0 0 0 0 X X X 0 X X 0 0 0 0 X 0 X 0 0 X X X 0 X 0 X X X X X 0 0 0 0 X 0 X X 0 0 0 0 X 0 X 0 0 X X 0 X 0 0 0 X 0 X X 0 X X X 0 0 X X X X 0 X 0 0 0 X X 0 0 X 0 0 X 0 0
0 0 0 X 0 0 0 0 0 X 0 X 0 X X 0 0 X 0 0 X 0 X 0 X 0 X 0 0 X X 0 0 X X 0 X 0 X 0 X 0 0 X X 0 X X 0 X X 0 0 X X 0 X 0 X X 0 X 0 0 0 0 0 X 0 X 0 X X 0 0 X 0 X 0 0 0 X 0 X 0 X X 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 X 0 0 0 X 0 0 0 X 0 X X X X 0 X 0 0 X 0 X 0 0 0 X X X 0 0 X 0 X 0 0 X 0 0 X X 0 X 0 0 0 0 0 X 0 X 0 X X X X 0 X X 0 0 X 0 X X 0 0 X
0 0 0 0 0 X 0 0 0 X 0 0 X X X X 0 0 0 X 0 0 X X X X X X 0 0 0 X 0 0 0 0 0 X 0 X 0 0 X X 0 X 0 X X X 0 0 X X 0 0 X X X X 0 X X 0 0 0 0 0 X X X X 0 0 0 X X 0 0 0 X 0 0 X 0 0 X X 0
0 0 0 0 0 0 X 0 0 X 0 X X 0 0 0 X 0 X 0 X 0 X X X 0 0 X X 0 X X X X X 0 0 0 X X X 0 0 X X 0 0 0 0 0 0 X 0 0 X 0 0 X X X X 0 X 0 X 0 0 X 0 0 0 0 X X 0 0 X 0 X 0 0 0 X 0 X X X X 0
0 0 0 0 0 0 0 X 0 X X X 0 0 0 X 0 0 X X 0 0 X X 0 0 X X X 0 0 0 0 X X 0 X X 0 0 X X X 0 0 X 0 0 X 0 X X 0 X 0 X 0 X X 0 X 0 X X X 0 0 X 0 X 0 X 0 X 0 0 0 X 0 0 0 0 X X X 0 0 0 X
0 0 0 0 0 0 0 0 X X X 0 0 X 0 0 X X X 0 X X 0 0 X 0 0 0 X X 0 X 0 0 0 X X 0 X X X 0 0 X 0 X X 0 X X 0 X X X 0 0 X X X 0 X X X 0 0 X X 0 X 0 0 0 X 0 0 0 0 X X 0 X 0 0 0 0 0 0 0 X
generates a code of length 89 over Z2[X]/(X^2) who´s minimum homogenous weight is 80.
Homogenous weight enumerator: w(x)=1x^0+172x^80+104x^84+358x^88+184x^92+150x^96+50x^104+4x^112+1x^160
The gray image is a linear code over GF(2) with n=178, k=10 and d=80.
This code was found by Heurico 1.16 in 81.4 seconds.