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  1  0  0  1  1  1  1  X  1  0  X  1  1  X  1  1  1  1  0  1  1  0  1  0  1  X  1  1  1  1  1  0  0  0  1  1  1  X  1  1  1  1  1  1  1  1  1  1  0  1  1  1  1  X  X  X  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  0  1  1  0 X+1  0  1  1  0  1  1 X+1  0  1 X+1  1  X  1  1  0 X+1  1  0  1  1  1  X X+1  1  0 X+1  1  1  1  X  1  1  1  0 X+1 X+1  0  X  0  1  X  1 X+1  X  0 X+1 X+1  X  1  X  1 X+1  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  X  0  0  X  0  X  X  X  0  X  0  X  0  X  0  X  X  0  X  X  X  0  X  0  X  X  0  0  0  0  0  X  X  X  0  0  X  0  X  0  0  0  X  X  X  X  0  0  0  X  X  0  0  0  0  X  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  0  X  X  0  X  X  0  X  0  X  0  0  X  0  X  0  X  0  X  X  0  0  X  X  X  0  0  X  0  0  0  X  X  X  0  0  0  X  X  0  0  X  0  0  X  0  X  X  0  X  X  0  0  X  0  0  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  X  X  0  0  X  X  0  0  X  0  0  X  0  X  0  0  X  0  0  X  0  X  X  0  0  X  X  X  X  0  X  0  X  0  0  0  0  X  X  0  0  X  0  0  X  0  0  0  0
 0  0  0  0  0  X  0  0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  X  0  X  X  X  X  0  0  X  X  X  0  X  0  0  X  X  X  0  0  X  0  X  X  X  X  X  X  0  0  X  0  X  0  X  X  X  X  0  X  X  X  X  X  X  0  X  0  0  0
 0  0  0  0  0  0  X  0  0  0  0  0  0  X  0  0  X  0  X  0  0  X  0  X  X  X  X  0  0  X  0  X  X  0  0  X  0  0  X  X  X  X  0  X  X  X  X  0  X  0  X  0  X  X  X  X  0  0  0  0  0  0  X  0  0  0  X  X  0  0  X  0  X  X  X  0  0  0  0  X  X  0
 0  0  0  0  0  0  0  X  0  0  X  0  0  0  X  X  X  0  X  0  X  X  0  0  X  0  0  X  X  X  0  0  0  X  X  0  0  0  X  X  X  0  0  0  X  0  0  X  X  X  X  0  0  X  X  X  X  X  X  0  X  X  X  X  0  0  0  0  0  X  0  0  X  X  0  X  0  0  0  0  0  0
 0  0  0  0  0  0  0  0  X  0  0  X  0  X  X  0  X  X  0  X  X  X  0  0  X  0  X  0  0  X  X  0  0  0  X  X  0  0  X  0  0  0  X  X  X  0  0  0  X  X  X  X  0  0  X  0  0  0  0  0  X  X  X  X  0  0  X  X  X  0  X  0  0  0  0  0  X  X  0  0  0  0
 0  0  0  0  0  0  0  0  0  X  0  0  X  X  X  X  0  0  X  X  X  0  X  0  X  X  X  X  X  X  X  X  0  X  X  0  X  0  0  X  X  X  X  0  0  X  0  0  X  0  0  X  X  X  X  0  X  0  X  0  0  X  X  0  0  0  X  X  0  0  0  0  0  X  0  0  0  X  0  0  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+56x^68+56x^70+48x^71+155x^72+76x^73+167x^74+178x^75+174x^76+220x^77+186x^78+244x^79+184x^80+242x^81+176x^82+276x^83+176x^84+264x^85+156x^86+200x^87+152x^88+176x^89+153x^90+74x^91+78x^92+44x^93+74x^94+4x^95+31x^96+2x^97+27x^98+12x^100+24x^102+5x^104+4x^106+1x^114

The gray image is a linear code over GF(2) with n=164, k=12 and d=68.
This code was found by Heurico 1.16 in 4.19 seconds.