The generator matrix

 1  0  0  0  0  1  1  1  0  1  1  X  1  0  1  0  0  1  X  1  1  X  0  X  1  X  1  1  X  X  1  1  1  1  1  0  X  X  0  X  X  1  X  0  1  1  X  1  X  X  1  1  0  1  1  1  1  X  X  0  1  1  0  X  X  1  1  X  1  1  1  1  0  1  1  1  1  X  X  1  X  1  1  0  1  1  1  1  1
 0  1  0  0  0  0  0  0  0  1  1  1  1  1 X+1  X  1  1  1  1  X  0  1  0  X  1  0 X+1  0  X  1 X+1  X  0  X  1  1  1  0  1  1 X+1  1  X  0 X+1  1  X  1  X X+1  X  X  X X+1  X  1  1  0  X  0  X  0  1  0  0  X  X  1 X+1 X+1 X+1  1 X+1  X  X  1  1  0  1  0 X+1 X+1  X  X X+1  X  1 X+1
 0  0  1  0  0  0  1  1  1  1 X+1  0  0 X+1  X  0 X+1  1  X X+1  0  1  X  1  0 X+1 X+1  0  1  1  1 X+1  0  1  0  X  0  X  X  1  1 X+1  1  1  1  1 X+1  0  1  X  0  1  X  1  1  0  1  0  1  1  0  X  X X+1  X  1  X  1  1  X X+1 X+1 X+1  X  1 X+1 X+1  X  1  1  1 X+1  X  X  0  0 X+1 X+1 X+1
 0  0  0  1  0  1  1  0  1  X X+1  1  0  1  1  X  X  X X+1  1  1 X+1  X  X  0  0  1  0  1  0  0  1  0  0 X+1  1  0 X+1  1  X  0 X+1  1  0 X+1 X+1  X  X  1  1  1 X+1  1  X  X X+1  X  X  1  1  0  0  1 X+1  X  X  0  0 X+1 X+1  0  X  X  0  X  X  0  X  0  1  0  X X+1  1  X  X  1 X+1  0
 0  0  0  0  1  1  0  1 X+1  X X+1 X+1  1  X  0  1  1  0 X+1  1 X+1  1  X  0  0  1 X+1  1  X  1  1  X X+1  1  X  X X+1  0 X+1  0  0  1  X X+1  X  X  1  X  1  0 X+1  1  0  1 X+1  X  X  1  0  0 X+1 X+1  0  X  1  X  0 X+1  X X+1  1  1 X+1  0  1 X+1  X  X  X X+1  1 X+1  0  1  X X+1  1  1  0
 0  0  0  0  0  X  0  0  X  0  X  X  X  X  0  X  0  X  0  0  0  0  X  X  X  X  X  X  0  X  X  0  0  X  0  X  0  0  0  0  X  X  X  X  X  X  X  X  0  X  X  X  X  0  X  X  0  X  X  0  X  X  0  X  0  0  0  X  0  0  0  0  0  X  0  X  X  X  X  0  0  X  X  0  X  0  0  0  0
 0  0  0  0  0  0  X  0  0  0  0  0  X  0  0  X  X  X  X  0  0  X  0  0  X  0  X  0  X  X  0  0  X  X  0  0  X  0  0  X  X  0  X  X  0  X  0  0  0  X  X  0  0  X  X  X  0  X  0  0  0  X  X  0  X  X  X  0  X  X  0  0  0  X  0  X  0  0  X  X  X  0  X  X  X  X  0  X  0
 0  0  0  0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  0  0  X  0  X  X  X  0  X  X  0  0  X  X  X  0  0  X  0  X  0  0  X  X  X  0  X  0  0  0  X  0  X  X  0

generates a code of length 89 over Z2[X]/(X^2) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+55x^76+88x^77+166x^78+222x^79+296x^80+348x^81+348x^82+366x^83+436x^84+458x^85+401x^86+426x^87+421x^88+410x^89+395x^90+446x^91+376x^92+372x^93+345x^94+330x^95+272x^96+236x^97+284x^98+186x^99+158x^100+102x^101+77x^102+62x^103+25x^104+30x^105+29x^106+10x^107+7x^108+4x^109+3x^110+1x^112

The gray image is a linear code over GF(2) with n=178, k=13 and d=76.
This code was found by Heurico 1.16 in 15 seconds.