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

generates a code of length 82 over Z2[X]/(X^2) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+61x^68+132x^69+223x^70+366x^71+402x^72+468x^73+594x^74+610x^75+666x^76+758x^77+880x^78+886x^79+756x^80+888x^81+937x^82+920x^83+922x^84+882x^85+901x^86+742x^87+598x^88+616x^89+576x^90+430x^91+346x^92+286x^93+218x^94+118x^95+79x^96+60x^97+21x^98+24x^99+4x^100+6x^101+2x^102+4x^104+1x^132

The gray image is a linear code over GF(2) with n=164, k=14 and d=68.
This code was found by Heurico 1.10 in 15.3 seconds.