The generator matrix

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

generates a code of length 87 over Z2[X]/(X^2) who´s minimum homogenous weight is 71.

Homogenous weight enumerator: w(x)=1x^0+34x^71+116x^72+272x^73+398x^74+438x^75+646x^76+760x^77+931x^78+1084x^79+1137x^80+1250x^81+1365x^82+1632x^83+1657x^84+1792x^85+1877x^86+1756x^87+1949x^88+1864x^89+1698x^90+1782x^91+1489x^92+1362x^93+1191x^94+950x^95+856x^96+642x^97+566x^98+388x^99+267x^100+212x^101+143x^102+110x^103+67x^104+36x^105+20x^106+16x^107+5x^108+2x^109+2x^110+2x^111+2x^112+1x^114

The gray image is a linear code over GF(2) with n=174, k=15 and d=71.
This code was found by Heurico 1.11 in 77.4 seconds.