The generator matrix

 1  0  0  0  0  1  1  1  0  1  1  0  0  X  1  1  1  1  0  1  X  1  0  1  0  X  1  0  1  0  1  0  X  X  1  1  X  0  1  0  1  X  X  1  1  0  1  X  1  1  1  1  0  1  1  1  1  0  1  1  X  0  X  X  0  0  1  1  1  0  1  1  1  0  0  0  1  X  1  0  1  1
 0  1  0  0  0  0  0  0  0  1  1  1  1  1  1  X X+1  1  X  X  1  X  X  0  1  1 X+1  0 X+1  1  X  1  0  1  0  X  X  0 X+1  X X+1  1  1  0  1  0  1  1  X  X  X  1  0 X+1  X  X X+1  0 X+1  X  X  1  1  1  1  0  0  X  1  1  1  1  0  1  1  X  1  X X+1  0  0  1
 0  0  1  0  0  0  1  1  1  1  X  1  0 X+1 X+1 X+1  X X+1  0  0  X  0  1  1 X+1 X+1  0  1  1  X  0 X+1  X X+1  X X+1  1  1  0  X  1  X  1  X  1  1 X+1 X+1  1  1  1  X  X  0  0 X+1  0  1  0 X+1  1  0  1 X+1  1  0  X  0  1  X X+1  X  X  1  1  X  X  1  X  1  1  0
 0  0  0  1  0  1  1  0  1  0 X+1 X+1  1  X X+1 X+1  X  0  1  1  0  X  0  X  0 X+1 X+1 X+1  1  X  0  0  1 X+1 X+1  1  X  1  X  0  X X+1  X  1 X+1  1 X+1  1  0  1  X  X  0  1  1 X+1  1  1  0  X X+1  X  X  X  X  X X+1 X+1  0 X+1  1 X+1  1  0  1  1  X X+1 X+1  0  1  1
 0  0  0  0  1  1  0  1  1  X  0  X  1 X+1 X+1  0 X+1  X  0 X+1  0  X  X  1  1 X+1 X+1  X  X X+1  1  0 X+1 X+1  X X+1  1 X+1  X  1  1  0 X+1 X+1  0  0 X+1 X+1  0  1  1  1  1  X  X X+1  0  0 X+1  0 X+1 X+1  0  X X+1  1 X+1  0 X+1 X+1  X  X  X X+1  X X+1  0  0  X  1  X  0
 0  0  0  0  0  X  0  0  0  X  0  X  X  0  X  X  0  0  X  0  X  0  X  0  X  0  0  X  X  X  0  X  0  0  X  0  X  X  X  X  0  0  X  0  X  X  X  0  0  0  X  0  X  0  0  X  0  0  X  0  0  X  0  X  X  0  0  X  X  X  0  0  0  0  X  X  0  0  0  0  X  X
 0  0  0  0  0  0  X  0  0  0  0  0  0  0  X  0  0  0  0  0  X  X  X  X  X  0  0  X  X  X  0  0  X  X  X  0  0  X  0  0  0  X  0  0  0  X  0  X  0  0  0  X  0  X  X  X  X  0  0  X  0  X  X  X  X  0  X  X  X  0  0  X  0  0  0  X  X  X  0  0  0  0
 0  0  0  0  0  0  0  X  0  0  X  X  X  0  X  0  X  X  X  X  0  0  0  0  0  X  0  X  0  X  0  0  0  0  0  0  0  0  X  X  0  X  X  X  X  0  0  0  0  X  X  X  0  X  0  X  X  X  0  X  X  0  0  0  X  0  0  X  0  X  0  0  X  X  0  X  0  X  0  X  0  0
 0  0  0  0  0  0  0  0  X  X  X  0  X  X  X  X  0  X  0  0  X  0  X  X  0  0  X  0  X  X  X  X  X  X  0  0  X  X  X  0  0  0  0  X  X  0  X  0  X  X  0  X  0  0  X  0  X  X  X  X  X  X  X  0  0  X  0  X  X  0  X  0  0  0  X  X  X  X  X  X  X  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+76x^68+138x^69+214x^70+272x^71+490x^72+450x^73+547x^74+638x^75+653x^76+794x^77+792x^78+918x^79+868x^80+906x^81+990x^82+922x^83+870x^84+888x^85+768x^86+786x^87+658x^88+626x^89+533x^90+430x^91+346x^92+254x^93+196x^94+118x^95+101x^96+34x^97+48x^98+10x^99+30x^100+6x^101+6x^102+2x^103+1x^104+2x^106+1x^108+1x^120

The gray image is a linear code over GF(2) with n=164, k=14 and d=68.
This code was found by Heurico 1.16 in 96.4 seconds.