The generator matrix

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

generates a code of length 89 over Z2[X]/(X^2) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+75x^74+182x^76+262x^78+458x^80+547x^82+786x^84+882x^86+959x^88+965x^90+867x^92+745x^94+519x^96+405x^98+221x^100+145x^102+66x^104+52x^106+23x^108+13x^110+10x^112+4x^114+1x^116+1x^118+3x^120

The gray image is a linear code over GF(2) with n=178, k=13 and d=74.
This code was found by Heurico 1.16 in 57.7 seconds.