The generator matrix

 1  0  0  1  1  1  0  1  1  1  1  0  X  X  1  1  1  X  0  1  X  X  1  1  1  1  1  0  0  0  1  1  1  1  1  0  1  1  1  1  1  X  1  1  0  0  1  1  0  0  1  0  1  1  0  1  X  X  X  0  1  X  1  0  0  X  X  X  1  X  0  1  X  X  0  1  1  1  1  1  1  1  X  X  1  1  0
 0  1  0  1  0  1  1  0  0  1 X+1  1  X  1  0  X X+1  1  1  1  0  1  1  X  0  1 X+1  0  1  X  1  X  0  X  0  1  1 X+1  0  0  0  X  X  X  1  1 X+1  1  0  1  0  1 X+1 X+1  1 X+1  1  1  1  X X+1  1  0  1  1  1  X  0  0  1  1  0  0  1  X  0  1  0 X+1  0  X  1  0  1 X+1  0  1
 0  0  1  1  1  0  1  0  1  1  0  X  1 X+1 X+1  X  0  1  0 X+1  1  1 X+1 X+1  0  0  X  1  0  1  1  X X+1  0 X+1  X  1  1  X  0  0  1  0 X+1  0  1  0  X  1  0  1  0 X+1  X X+1  0  X  1  X  1 X+1  1  1  0  X X+1  1  1 X+1 X+1  1  0  1  0  1 X+1  1  X  1 X+1  X X+1  1 X+1  0  1  0
 0  0  0  X  0  0  0  0  0  0  0  0  0  X  X  X  X  X  0  X  X  0  X  0  0  X  X  0  0  X  0  X  0  0  X  0  X  X  X  0  X  0  X  X  X  X  X  0  0  X  0  0  X  X  0  0  0  0  X  0  0  X  0  0  0  0  0  0  0  X  0  0  X  X  X  X  X  0  0  X  0  X  X  0  0  0  X
 0  0  0  0  X  0  0  0  0  0  X  X  X  0  X  X  0  X  X  X  X  X  0  X  0  X  0  X  0  X  0  0  0  X  0  X  X  X  0  X  X  X  X  0  0  0  X  0  0  X  X  0  X  0  0  0  0  0  X  0  0  X  X  0  0  0  X  X  X  0  X  0  0  X  0  X  0  0  0  0  X  0  X  X  0  0  X
 0  0  0  0  0  X  0  0  0  0  X  0  0  0  0  0  X  0  0  0  0  0  0  0  0  X  X  X  0  X  X  X  X  X  X  X  0  0  0  X  0  0  0  X  X  X  X  X  X  X  0  X  X  0  0  X  0  X  0  0  X  X  0  0  X  X  0  0  X  0  0  0  X  0  X  X  X  0  X  0  0  X  X  0  X  0  X
 0  0  0  0  0  0  X  0  0  0  0  0  0  X  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  X  0  X  0  0  0  X  X  0  X  0  0  0  0  X  X  0  X  X  0  X  X  0  0  0  X  X  X  0  X  0  0  X  X  0  X  0  0  X  0  X  X  X  X  0  X  X  0  0  0  0  0  0  X  0  X  X  0
 0  0  0  0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  0  X  X  0  0  X  0  X  X  0  0  X  X  X  X  X  X  X  X  0  X  0  X  0  0  0  0  X  0  X  0  0  X  0  X  0  X  X  X  0  0  X  X  0  0  0  0  0  X  X  0  X  X  X  0  0  0  X  0  0  X  0  X  X
 0  0  0  0  0  0  0  0  X  0  X  X  X  0  0  X  0  X  X  X  X  X  0  0  0  X  0  X  X  X  0  0  X  X  X  X  0  0  X  0  0  0  0  0  X  0  0  0  0  0  X  X  X  X  X  X  0  X  X  0  X  0  X  X  X  0  X  0  X  X  0  X  0  0  X  0  X  0  X  X  X  X  X  X  X  0  0
 0  0  0  0  0  0  0  0  0  X  0  0  0  X  X  X  X  X  0  0  X  0  0  0  0  X  X  X  X  0  0  0  X  X  0  X  X  X  0  0  0  X  0  X  X  0  X  X  0  0  0  X  0  X  X  0  X  X  X  X  0  0  0  0  0  0  X  X  X  X  X  X  0  X  X  0  X  X  0  0  X  0  X  X  X  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+129x^74+364x^76+489x^78+658x^80+782x^82+794x^84+890x^86+911x^88+904x^90+788x^92+571x^94+389x^96+231x^98+143x^100+76x^102+39x^104+17x^106+6x^108+6x^110+2x^112+1x^114+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 39.8 seconds.