The generator matrix

 1  0  0  0  1  1  1  0  1  1  1  1  X  X  X  1  0  X  0  1  0  1  1  1  X  0  0  1  1  1  X  1  1  0  1  1  1  0  0  1  1  X  X  0  1  1  1  X  1  1  1  1  1  X  0  0  0  1  1  1  0  1  0  0  X  1  X  0  1  X  X  X  0  1  1  X  1  1  1  1  X  1  0  1  X  1  1
 0  1  0  0  0  1  1  1  0  X X+1 X+1  1  1  X  0  0  0  1  X  1 X+1  1  1  0  0  1  0  X X+1  X  X  0  1  X  0 X+1  0  1  X  0  1  1  1  0  1  X  1 X+1 X+1  1 X+1 X+1  0  1  1  X  X X+1  0  X  0  1  1  1 X+1  1  1  1  X  0  1  0 X+1  0  1  X  X  X  1  1  X  0  1  1  1  0
 0  0  1  0  1  1  0  1  0  1  1  X  0  1  1  X  1  X  X  1  1 X+1  0  1  1  1  0  0  1  X  1  0  1  X  0  1 X+1  1 X+1  1  1 X+1 X+1  X X+1  0  0  X  X  X  1  1 X+1  1  X X+1  0 X+1  1  X  0 X+1  0  0  1  X X+1 X+1 X+1  X  1  0  X  X  X  0  X  0 X+1  0  1  0  1  0  1  0  0
 0  0  0  1  1  0  1  1  1  0 X+1  X  1  X  1 X+1  0  1  0 X+1  0  0  1 X+1  0  X  1  X  0  X  1  1  0  1  0  X  0  1  1 X+1  1  X X+1  1  0  X  1  X  0 X+1  1  X  0  0  X X+1  1 X+1  1  0  1 X+1  1  0  X  X  1  0 X+1  1  1 X+1  1 X+1  0  0  1  X  1  1 X+1  X  X  X  X  0  0
 0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  0  0  X  X  X  X  0  X  0  0  X  0  0  X  X  0  0  0  0  X  0  0  0  X  X  X  X  X  0  X  X  0  X  X  0  0  X  X  0  X  X  X  0  0  0  0  X  X  0  0  X  0  X  X  X  X  X  X  0  X  0
 0  0  0  0  0  X  0  0  0  0  0  0  X  0  X  X  X  X  X  X  X  0  0  0  X  0  0  X  X  0  X  0  X  0  0  X  0  X  0  X  0  0  X  X  0  0  X  X  0  0  X  0  0  X  0  X  X  0  X  0  0  0  X  X  X  X  0  0  X  0  X  0  X  X  0  0  0  0  0  0  X  X  0  0  X  0  0
 0  0  0  0  0  0  X  0  0  0  0  0  0  X  0  X  X  X  0  X  X  0  0  X  0  X  X  0  0  0  0  0  0  X  0  0  X  X  X  X  0  X  X  0  X  0  X  X  0  X  0  X  0  X  X  0  X  X  X  X  X  0  X  X  X  0  0  X  X  0  X  0  X  X  0  X  X  X  X  X  X  0  X  X  0  X  0
 0  0  0  0  0  0  0  X  0  0  X  0  X  X  0  X  X  0  0  X  X  X  X  0  0  X  X  0  X  X  0  X  X  0  X  0  X  0  X  X  X  0  X  X  0  0  X  0  0  X  0  0  0  0  0  0  0  0  X  0  0  X  X  X  X  X  0  X  0  X  X  0  0  X  X  0  X  X  0  0  0  0  0  X  0  0  X
 0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  0  0  0  0  X  0  0  X  0  0  X  0  X  X  X  X  X  X  0  X  0  X  0  X  X  0  X  0  0  0  0  X  0  X  0  X  X  X  X  X  0  0  X  0  X  0  X  0  X  0  X  X  0  X  0  0  X  0  X  0  0  0  0  X  X  0  X  X  X  0  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+60x^74+78x^75+155x^76+232x^77+307x^78+330x^79+376x^80+392x^81+337x^82+388x^83+447x^84+412x^85+447x^86+468x^87+391x^88+436x^89+426x^90+408x^91+336x^92+336x^93+272x^94+282x^95+232x^96+192x^97+141x^98+68x^99+80x^100+44x^101+43x^102+24x^103+21x^104+4x^105+12x^106+2x^107+5x^108+3x^110+3x^112+1x^116

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 14.9 seconds.