The generator matrix

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

generates a code of length 86 over Z2[X]/(X^2) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+185x^72+92x^74+509x^76+352x^78+811x^80+672x^82+1111x^84+820x^86+1085x^88+700x^90+756x^92+360x^94+409x^96+72x^98+160x^100+4x^102+65x^104+23x^108+3x^112+1x^116+1x^120

The gray image is a linear code over GF(2) with n=172, k=13 and d=72.
This code was found by Heurico 1.16 in 36.4 seconds.