The generator matrix

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

generates a code of length 82 over Z2[X]/(X^2) who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+76x^67+217x^68+328x^69+494x^70+644x^71+720x^72+870x^73+1034x^74+1156x^75+1330x^76+1454x^77+1597x^78+1672x^79+1779x^80+1904x^81+1943x^82+1938x^83+1880x^84+1840x^85+1665x^86+1582x^87+1397x^88+1192x^89+1002x^90+814x^91+652x^92+464x^93+376x^94+250x^95+180x^96+122x^97+60x^98+56x^99+31x^100+18x^101+19x^102+4x^103+3x^104+2x^108+1x^110+1x^114

The gray image is a linear code over GF(2) with n=164, k=15 and d=67.
This code was found by Heurico 1.11 in 74.3 seconds.