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

generates a code of length 87 over Z2[X]/(X^2) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+76x^74+70x^75+156x^76+248x^77+302x^78+350x^79+370x^80+390x^81+378x^82+402x^83+395x^84+428x^85+406x^86+436x^87+412x^88+414x^89+390x^90+386x^91+361x^92+312x^93+316x^94+278x^95+233x^96+194x^97+128x^98+102x^99+103x^100+52x^101+40x^102+24x^103+14x^104+10x^105+12x^106+1x^108+2x^112

The gray image is a linear code over GF(2) with n=174, k=13 and d=74.
This code was found by Heurico 1.16 in 14.3 seconds.