The generator matrix
1 0 0 1 1 1 0 1 1 1 1 0 X 0 1 1 0 1 X 1 X 1 1 X 0 0 0 1 1 1 1 1 0 1 0 X X X 0 1 1 1 X 1 1 0 0 X X 1 1 0 0 1 1 0 X 1 1 0 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 X X 1 1 X 0 0 1 1 0 0 1 0 1
0 1 0 0 1 1 1 0 0 1 X+1 1 1 X X X 0 1 1 X+1 1 1 1 1 1 0 0 X X X+1 X+1 X+1 0 X+1 1 1 1 1 1 0 X 1 0 X+1 X+1 1 1 1 1 X 1 1 1 1 0 X 0 X+1 X 1 0 0 0 1 0 1 X 0 1 1 0 1 X 0 0 X X X 0 0 1 1 0 X 0 1 X 1 X+1
0 0 1 1 1 0 1 0 1 X+1 0 X X+1 1 X 1 1 1 X 0 X+1 X+1 0 0 1 1 1 X 1 X+1 X+1 1 1 1 0 X X+1 1 1 0 1 X 1 0 0 X+1 0 1 1 1 0 X X 0 X 1 1 0 X+1 X X+1 1 0 X+1 1 X+1 0 X+1 1 0 1 X X 0 X 1 1 0 X 1 X 1 0 0 1 X+1 X+1 X+1 X
0 0 0 X 0 0 0 0 0 X X 0 0 X X 0 X 0 0 0 0 X X 0 0 X X X X 0 X X 0 0 0 X 0 0 X X 0 X X 0 0 0 X 0 X X X 0 0 X X 0 0 X 0 X X X 0 0 0 X 0 X 0 X 0 X 0 X X X X X 0 X 0 0 0 0 0 0 0 X X
0 0 0 0 X 0 0 0 0 X 0 0 0 0 0 0 0 X 0 0 0 X 0 0 0 0 0 0 0 X X X 0 X 0 0 0 0 0 0 0 0 0 X X X X X X X 0 X X X X X X X X X 0 X 0 X X 0 X X X 0 X 0 X 0 X 0 X 0 X 0 X 0 0 0 X X X 0 0
0 0 0 0 0 X 0 0 0 0 X 0 0 0 0 0 0 0 0 X 0 0 X 0 0 0 0 0 0 0 0 0 0 0 X X X X X X X 0 X X X X X X 0 X 0 0 X X X 0 0 X X X X 0 X X X X 0 X X X 0 0 0 0 X 0 X X X X 0 X X X X 0 X 0 0
0 0 0 0 0 0 X 0 0 0 0 0 X 0 0 0 0 0 0 0 X 0 0 0 X X X X X X X X 0 X X X X X X X 0 X 0 X 0 0 X X X 0 0 X 0 0 X X 0 0 X X 0 X X X 0 X X 0 X X 0 0 0 0 X X X 0 X X 0 0 X 0 0 X X X X
0 0 0 0 0 0 0 X 0 0 0 X X 0 X X X X 0 0 X X 0 X 0 0 X 0 X 0 X X X 0 X X X 0 0 X X 0 0 0 0 X X X 0 0 X 0 0 X X X 0 0 X 0 0 X 0 0 X X 0 X 0 0 0 X X 0 0 0 X X X 0 X 0 X 0 0 0 X 0 0
0 0 0 0 0 0 0 0 X X X 0 0 0 X X X X X X X 0 0 X X 0 X X 0 X X 0 0 0 X X 0 X X X 0 0 0 X 0 0 X 0 0 0 X X X X 0 0 0 X X 0 X 0 0 X X 0 X X X X X 0 0 X X X X 0 0 X 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 78.
Homogenous weight enumerator: w(x)=1x^0+156x^78+269x^80+406x^82+450x^84+466x^86+419x^88+375x^90+430x^92+330x^94+296x^96+205x^98+118x^100+86x^102+53x^104+17x^106+10x^108+2x^110+2x^112+5x^114
The gray image is a linear code over GF(2) with n=178, k=12 and d=78.
This code was found by Heurico 1.16 in 19.6 seconds.