The generator matrix

1 0 0 0 0 1 1 1 0 1 1 X 0 1 1 X 0 1 1 X 0 1 0 1 1 0 1 X 1 X 1 X 1 1 X X 1 X 0 1 1 0 X 1 1 1 1 0 0 X 0 X 1 1 0 0 1 0 X X X 1 0 1 1 1 X 0 X 1 1 X X X 0 1 0 1 1 1 1 0 1 0 1 1 1 0 1
0 1 0 0 0 0 0 0 X 0 X X X 0 X 0 X 1 X+1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 X 1 1 X X+1 X 1 0 1 X X 1 0 0 1 0 X+1 X 1 1 0 X 0 X 1 0 0 1 X 0 1 1 1 X X+1 1 0 X X X 0 X 1 X+1 1 1 1 0 X+1 X+1 1 0 0
0 0 1 0 0 0 0 X 0 1 1 1 1 1 X+1 1 X X 1 X 1 X+1 1 0 0 X X+1 X 0 1 X+1 1 1 X+1 X+1 1 X+1 0 0 0 X 0 X X X X X X+1 1 1 X 1 0 1 1 X+1 X 1 0 1 0 1 1 X X 0 X+1 1 1 0 X+1 X+1 1 X 1 X 1 0 1 X 0 X X X 1 X+1 X 1 0
0 0 0 1 0 1 0 1 1 1 0 X 1 X+1 0 X+1 X 1 X X+1 X X+1 X+1 1 X 0 X+1 X+1 0 1 X 0 X+1 X+1 1 X+1 0 0 X X+1 1 1 1 X X X+1 X 0 X+1 X 0 0 0 1 1 1 0 0 1 X X 0 X+1 1 X X+1 X+1 X 1 0 X 1 X 1 0 0 1 X 0 X X+1 1 X 1 X+1 1 X+1 1 1
0 0 0 0 1 1 X+1 0 1 X X X+1 0 X+1 1 1 1 X+1 1 X X 0 1 0 X 1 X+1 X+1 1 0 0 1 1 X+1 0 X+1 1 0 1 1 X 1 X 0 X+1 X 1 1 X 0 X+1 X+1 X+1 X 1 X X+1 0 X X+1 X+1 0 1 1 0 0 X+1 0 X+1 X 1 0 X+1 1 0 X+1 X+1 1 X+1 X+1 1 0 X X X X 1 0 0
0 0 0 0 0 X X 0 X 0 0 X 0 X X X X X X 0 0 0 X 0 0 X X X X 0 X 0 0 0 X 0 0 X 0 0 X 0 X X 0 X 0 0 X X 0 0 0 X 0 0 0 X X 0 0 X 0 0 X 0 0 X X X 0 0 0 X 0 X 0 0 X 0 X X X 0 X 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+97x^80+244x^82+323x^84+278x^86+237x^88+194x^90+180x^92+126x^94+93x^96+78x^98+80x^100+50x^102+36x^104+16x^106+9x^108+6x^110

The gray image is a linear code over GF(2) with n=178, k=11 and d=80.
This code was found by Heurico 1.10 in 0.297 seconds.