The generator matrix

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

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+53x^74+141x^76+240x^78+338x^80+405x^82+444x^84+481x^86+485x^88+418x^90+358x^92+301x^94+207x^96+98x^98+38x^100+27x^102+22x^104+17x^106+9x^108+7x^110+2x^112+1x^114+2x^116+1x^120

The gray image is a linear code over GF(2) with n=174, k=12 and d=74.
This code was found by Heurico 1.16 in 4.68 seconds.