The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  1  X  1  1  X  X  1  1  1  X  1  1  1  1  1  X  X  1  0  1  1  X  X  1  1  1  1  0  1  X  1  X  1  1  X  0  1  X  1  1  X
 0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  0  0  0  X  X  X  0  X  X  0  0  X  0  0  X  X  0  X  X  X  X  0  0  0  0  0  X  X  X  0  0  0  X  X  0  X  X  X  0  X  0  0  X  X  0  X  X  0  X  0  X  0  X  0  0  0  0  X  X  X  0  0  0  X  0
 0  0  X  0  0  0  0  0  0  0  0  0  X  0  0  X  X  X  X  X  X  0  0  0  0  0  0  0  0  X  0  X  X  X  X  X  X  X  0  X  0  0  X  0  X  0  X  X  X  0  0  0  X  0  0  0  0  X  0  X  0  X  0  X  0  X  X  X  X  X  0  0  0  0  0  0  0  X  X  0  X  X  X  X  X  X  0
 0  0  0  X  0  0  0  0  0  0  0  0  X  X  X  X  X  0  X  X  X  X  0  0  X  X  X  X  X  X  0  X  0  X  X  0  X  0  0  0  0  0  0  0  0  0  0  X  0  0  0  X  X  X  X  X  0  0  0  0  0  0  X  0  X  X  X  X  X  0  0  X  X  0  0  X  0  0  0  X  X  X  0  X  X  X  0
 0  0  0  0  X  0  0  0  0  0  0  X  0  X  X  0  X  X  X  0  X  0  X  0  X  0  0  X  0  X  0  0  0  0  0  X  X  0  0  X  0  0  0  X  0  0  X  X  X  X  X  X  0  X  X  X  X  0  0  X  0  0  X  X  0  X  0  0  0  0  X  0  0  X  0  0  0  0  0  X  X  X  X  X  0  X  X
 0  0  0  0  0  X  0  0  0  0  0  X  0  0  X  X  X  X  X  0  0  X  X  0  0  0  X  0  0  0  X  X  0  X  X  0  X  X  X  X  0  X  0  0  X  X  0  X  0  X  0  0  X  X  X  X  X  X  0  0  0  X  0  X  X  0  0  0  0  0  X  0  X  X  0  X  X  0  0  0  0  0  0  X  X  X  0
 0  0  0  0  0  0  X  0  0  0  X  0  0  0  X  X  0  0  X  0  0  X  X  0  X  X  X  0  X  X  X  0  0  0  0  X  X  0  X  0  X  0  0  X  0  X  X  X  X  X  0  0  X  0  X  0  0  0  X  0  X  X  X  0  X  X  X  0  0  X  0  0  X  X  0  0  X  X  0  X  0  0  0  X  0  0  0
 0  0  0  0  0  0  0  X  0  0  X  0  0  X  0  0  X  0  0  X  0  X  X  X  0  X  0  X  X  X  0  X  X  0  X  0  0  X  0  X  X  0  0  X  0  X  0  X  X  X  X  X  X  0  0  0  0  X  0  0  0  0  X  X  X  X  X  0  X  X  0  X  0  0  0  0  X  X  0  0  0  0  X  0  0  X  0
 0  0  0  0  0  0  0  0  X  0  X  X  X  X  0  0  0  0  X  0  0  0  0  X  X  0  0  X  X  0  X  0  X  0  0  X  0  0  X  X  X  0  0  X  X  0  X  0  X  0  0  0  X  0  0  X  0  X  0  X  X  0  0  0  X  X  0  X  X  0  0  0  X  X  0  X  X  X  X  X  X  X  0  X  0  X  X
 0  0  0  0  0  0  0  0  0  X  X  X  X  0  0  X  X  X  X  X  0  X  X  X  X  0  X  0  X  X  X  0  X  0  X  0  X  0  0  X  X  0  X  0  0  0  X  0  0  X  0  X  0  X  0  X  0  X  X  0  0  X  X  X  0  X  X  X  X  0  X  0  X  X  X  X  X  0  X  0  X  0  0  0  X  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+43x^74+87x^76+125x^78+162x^80+178x^82+224x^84+240x^86+247x^88+241x^90+160x^92+97x^94+63x^96+48x^98+49x^100+30x^102+22x^104+18x^106+7x^108+4x^110+1x^116+1x^136

The gray image is a linear code over GF(2) with n=174, k=11 and d=74.
This code was found by Heurico 1.16 in 1.54 seconds.