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 X X X X X X X X X X 1 X 0 1 X X X 1 X 0 X 1 1 1 0 1 0 X 1 1 1 1
0 X 0 0 0 0 0 0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 X X X X X X X 0 X X X X 0 X 0 0 0 X X X 0 X X X 0 X 0 X 0 X 0 X 0 0 X X 0 0 0 0 X 0 0 X 0 0 X 0 X X X 0 0 X X 0
0 0 X 0 0 0 0 0 0 0 0 0 0 0 X 0 0 0 0 X X X X X X X 0 0 0 X 0 0 0 X X X 0 0 0 X X X X 0 X 0 0 X X X 0 0 X 0 X X X 0 0 0 X X 0 0 0 X 0 X 0 X 0 0 0 X 0 X 0 X X 0
0 0 0 X 0 0 0 0 0 0 0 0 0 X 0 0 0 X X X X X X 0 0 0 0 X 0 X X X 0 X 0 0 X X 0 0 0 X X X 0 X 0 X X X X X 0 0 0 0 0 X 0 X 0 0 X 0 0 0 0 0 0 X 0 X X X 0 X 0 0 0 0
0 0 0 0 X 0 0 0 0 0 0 0 0 X 0 X X X X X X 0 X X 0 X X X 0 0 0 X X X X X 0 X X 0 0 0 0 X 0 0 0 X 0 0 0 0 0 X X X X X 0 0 X X 0 0 0 X 0 0 X X X 0 X 0 X X 0 0 0 0
0 0 0 0 0 X 0 0 0 0 0 0 X 0 0 X X 0 X X 0 X 0 X 0 X X X X 0 0 X X 0 0 0 X 0 X 0 0 0 X 0 X 0 X X X X 0 0 X 0 0 X 0 0 X 0 X 0 X X X X X 0 0 0 X X X 0 X X 0 0 0 0
0 0 0 0 0 0 X 0 0 0 0 0 X 0 0 0 X X X X 0 X X 0 X 0 X 0 0 X 0 0 X X X 0 0 0 0 X 0 0 X 0 X X X 0 X 0 0 X 0 0 0 X X X 0 X 0 0 X 0 X X X X X 0 0 0 0 X X 0 X X X 0
0 0 0 0 0 0 0 X 0 0 0 X 0 0 0 0 X X 0 X 0 0 0 X X X 0 0 X 0 X X X X 0 0 0 X X X X X 0 0 0 0 X X X X 0 X X X 0 0 X 0 0 X 0 X X 0 0 X X X 0 X X X X 0 X 0 X X X 0
0 0 0 0 0 0 0 0 X 0 0 X 0 0 0 X 0 0 X 0 X 0 0 X 0 0 0 0 X X X 0 0 X X 0 X X X X 0 0 X 0 X X X 0 X X X X 0 X 0 0 0 X X X 0 X X X X X 0 0 0 0 X 0 X 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 X 0 X X X X X 0 0 0 X 0 0 X X 0 0 X 0 X X 0 0 X X 0 X X 0 0 0 0 X 0 0 0 X 0 X 0 X X 0 X 0 X X X X 0 X 0 X 0 0 X 0 0 X X 0 0 X X 0 X 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 X X X X X 0 0 X X X X X 0 X 0 X 0 0 0 0 0 X 0 X 0 0 X 0 X X 0 0 X 0 0 0 X 0 0 0 0 X X X X X X X 0 X X X 0 X 0 0 X X X 0 0 X X X X 0 X X X 0
generates a code of length 80 over Z2[X]/(X^2) who´s minimum homogenous weight is 64.
Homogenous weight enumerator: w(x)=1x^0+60x^64+54x^66+4x^67+141x^68+22x^69+90x^70+52x^71+184x^72+120x^73+150x^74+208x^75+152x^76+278x^77+157x^78+344x^79+147x^80+336x^81+145x^82+276x^83+148x^84+210x^85+148x^86+116x^87+87x^88+56x^89+127x^90+24x^91+60x^92+2x^93+99x^94+32x^96+33x^98+11x^100+17x^102+1x^104+3x^106+1x^118
The gray image is a linear code over GF(2) with n=160, k=12 and d=64.
This code was found by Heurico 1.16 in 5.58 seconds.