The generator matrix

1 0 0 0 0 0 0 1 1 1 X 1 1 0 1 1 0 0 1 1 0 1 0 1 X X X 1 X 1 0 1 1 1 0 0 1 1 X 1 1 X 1 1 1 0 0 X X 0 0 1 1 1 1 1 1 0 1 0 1 0 1 1 X 1 1 0 0 1 1 1 X X X 1 1 X 1 0 1 1 X 1 X 1
0 1 0 0 0 0 0 0 0 0 0 0 0 0 X X X 1 X+1 1 1 1 1 X+1 1 1 1 X+1 0 X 1 X+1 X+1 1 1 1 X+1 0 1 X X+1 X X+1 0 1 X 0 1 1 1 0 X+1 0 1 1 X+1 X+1 1 X+1 1 0 X 0 X+1 1 1 0 X 1 X 1 X+1 X X 0 X 0 0 0 X X+1 X 0 X 1 0
0 0 1 0 0 0 0 0 0 0 0 0 0 X 0 0 X 0 0 0 0 X X X X 0 X X X X X 0 0 X 0 0 1 X+1 X+1 X+1 X+1 1 1 X+1 1 1 1 1 X+1 1 1 X+1 X+1 1 X+1 X+1 X 1 1 0 1 1 X+1 X+1 1 X+1 X+1 1 X+1 X X 1 X 1 1 X X 0 X+1 X X 0 X X X+1 0
0 0 0 1 0 0 0 0 0 X X 1 1 1 1 X+1 1 1 X X+1 1 0 X X+1 X X X+1 X+1 1 1 X+1 X X+1 X X+1 1 X X 1 0 0 1 0 X+1 X+1 1 X X+1 1 0 X+1 1 1 1 X+1 1 1 X X+1 X+1 X X 0 1 0 1 0 X+1 1 X X+1 0 0 0 X 1 X+1 1 X+1 1 X X 1 X+1 1 0
0 0 0 0 1 0 0 1 X 1 1 0 X+1 1 0 1 0 1 X 1 X+1 0 0 X 1 1 X 0 X+1 X X X+1 X+1 X+1 X 0 1 X 0 1 0 X X X+1 1 X X+1 X+1 X+1 X+1 X+1 X X 1 X X 0 0 1 1 X+1 1 1 0 0 X 1 X 1 X 1 X 1 0 1 X 1 X 1 X X X+1 0 1 X 0
0 0 0 0 0 1 0 1 X+1 0 1 X X+1 1 1 0 1 X X+1 1 1 0 1 X+1 X 1 X+1 X X X+1 0 1 0 X X+1 X X 1 0 X 1 X X X X+1 1 0 X X+1 X X+1 X+1 0 X X+1 X X+1 X X X+1 X+1 0 X X 0 0 X+1 X X 1 1 1 X X+1 0 0 X X 1 X+1 X+1 X+1 0 1 X+1 X+1
0 0 0 0 0 0 1 X 1 1 X+1 1 X+1 0 0 X X+1 0 0 0 X+1 1 1 1 1 X 0 X X+1 0 X+1 X+1 1 0 X X+1 X+1 0 X 0 1 X+1 X X+1 1 X 1 X+1 0 X X+1 X 0 X X 1 X+1 1 1 0 0 0 X+1 0 0 X X 0 X 0 1 0 X+1 X+1 0 X X+1 X+1 0 X 1 X+1 0 X+1 1 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+67x^72+166x^73+283x^74+324x^75+416x^76+498x^77+531x^78+688x^79+678x^80+712x^81+774x^82+888x^83+887x^84+910x^85+943x^86+834x^87+885x^88+818x^89+791x^90+750x^91+692x^92+630x^93+534x^94+404x^95+349x^96+300x^97+178x^98+180x^99+109x^100+58x^101+55x^102+26x^103+12x^104+4x^105+6x^106+2x^107+1x^126

The gray image is a linear code over GF(2) with n=172, k=14 and d=72.
This code was found by Heurico 1.10 in 16.3 seconds.