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.