The generator matrix

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

generates a code of length 81 over Z2[X]/(X^2) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+42x^68+123x^70+257x^72+253x^74+559x^76+317x^78+598x^80+382x^82+575x^84+231x^86+385x^88+158x^90+90x^92+39x^94+33x^96+22x^98+13x^100+10x^102+4x^104+1x^106+1x^108+2x^112

The gray image is a linear code over GF(2) with n=162, k=12 and d=68.
This code was found by Heurico 1.16 in 4.25 seconds.