The generator matrix

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

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+170x^68+481x^70+793x^72+1036x^74+1356x^76+1603x^78+1786x^80+1847x^82+1909x^84+1711x^86+1364x^88+1025x^90+622x^92+367x^94+151x^96+105x^98+39x^100+12x^102+3x^106+2x^110+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 55.1 seconds.