The generator matrix

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

generates a code of length 86 over Z2[X]/(X^2) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+68x^69+181x^70+328x^71+564x^72+678x^73+942x^74+1054x^75+1282x^76+1638x^77+1955x^78+2320x^79+2707x^80+2944x^81+3176x^82+3518x^83+3663x^84+3894x^85+3648x^86+3676x^87+3693x^88+3558x^89+3421x^90+3116x^91+2640x^92+2374x^93+2082x^94+1620x^95+1352x^96+950x^97+783x^98+598x^99+399x^100+206x^101+156x^102+132x^103+75x^104+60x^105+37x^106+18x^107+8x^108+12x^109+1x^110+4x^111+2x^113+1x^114+1x^118

The gray image is a linear code over GF(2) with n=172, k=16 and d=69.
This code was found by Heurico 1.11 in 323 seconds.