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

generates a code of length 86 over Z2[X]/(X^2) who´s minimum homogenous weight is 73.

Homogenous weight enumerator: w(x)=1x^0+54x^73+111x^74+176x^75+225x^76+230x^77+334x^78+340x^79+370x^80+398x^81+371x^82+472x^83+451x^84+442x^85+446x^86+422x^87+443x^88+426x^89+383x^90+336x^91+331x^92+314x^93+271x^94+208x^95+169x^96+138x^97+98x^98+88x^99+45x^100+38x^101+20x^102+6x^103+8x^104+8x^105+12x^106+4x^108+1x^110+1x^114+1x^120

The gray image is a linear code over GF(2) with n=172, k=13 and d=73.
This code was found by Heurico 1.16 in 14.5 seconds.