The generator matrix

 1  0  0  1  1  1  0  1  1  1  1  0  X  X  1  1  1  1  X  0  0  1  1  0  1  X  X  1  X  1  X  1  1  1  1  0  X  1  1  1  1  X  1  1  1  1  X  1  1  X  X  0  1  0  X  1  0  1  1  1  0  1  1  X  1  1  1  1  X  0  1  1  X  1  1  1  X  X  1  X  X  1
 0  1  0  1  0  1  1  0  0  1 X+1  1  X  1  0  X  1 X+1  1  1  X  1  1  1  0  0  1  X  1  0  1 X+1 X+1  1  X  1  1  1  1  0  0  X  0 X+1  1  X  1  0 X+1  X  X  1 X+1  1  0  1  0  1  1 X+1  0  0  1  1  0  0  1  0  1  1 X+1 X+1  0  X  X  X  1  1  X  1  0  0
 0  0  1  1  1  0  1  0  1  1  0  X  1 X+1 X+1  X X+1  0  1  0  1  1  0  1  X  1  X  1  0  X X+1  X  X  1 X+1  0  X  1 X+1  1  X  1  0  1  X X+1  X  1  X  1  1  1  1  0  1  0  1  X  1 X+1  1 X+1  0  0 X+1  0 X+1 X+1  1 X+1  0  X  1  1  0 X+1  0  0  X  X  0  0
 0  0  0  X  0  0  0  0  0  0  0  0  0  X  X  X  X  X  0  0  X  X  X  X  X  0  X  X  X  0  X  0  X  X  X  0  X  X  X  X  0  0  X  X  X  0  0  0  X  X  X  X  X  0  0  0  X  X  0  0  0  0  X  0  X  0  X  0  0  0  0  X  X  0  X  X  0  X  X  X  0  0
 0  0  0  0  X  0  0  0  0  0  X  X  X  0  X  X  0  0  X  0  0  X  X  0  X  0  X  X  X  X  0  0  0  0  X  0  0  X  X  X  0  X  X  0  X  X  X  X  0  X  X  0  X  0  0  0  0  0  0  X  X  0  0  0  X  0  0  X  0  0  X  0  X  X  0  0  X  0  0  X  0  0
 0  0  0  0  0  X  0  0  0  0  X  0  0  0  0  0  0  X  0  0  0  0  X  0  0  0  0  0  0  0  0  X  X  0  0  X  X  X  X  X  X  X  X  X  X  0  X  X  0  X  0  X  X  0  0  X  X  0  0  0  0  X  X  0  0  X  0  X  X  0  0  X  X  0  X  X  X  0  X  0  X  0
 0  0  0  0  0  0  X  0  0  0  0  0  0  X  0  0  0  0  X  0  0  0  0  X  0  0  X  0  X  X  0  X  X  X  X  X  X  0  X  X  0  0  X  0  0  X  X  0  X  0  X  0  0  0  X  X  X  X  0  X  0  X  X  0  X  0  X  0  X  X  0  0  X  0  0  X  0  0  X  0  0  0
 0  0  0  0  0  0  0  X  0  0  0  0  0  0  0  0  X  X  X  X  X  X  0  X  0  0  X  X  0  0  0  X  X  X  0  X  X  X  0  0  X  X  X  0  X  X  0  X  X  0  0  X  0  0  X  X  0  0  X  X  X  X  X  X  0  X  0  X  0  X  X  X  0  X  0  X  X  X  0  X  X  0
 0  0  0  0  0  0  0  0  X  0  X  X  X  0  0  X  0  0  X  X  0  0  0  X  0  X  X  0  0  0  0  0  X  0  X  X  0  X  X  0  X  X  0  0  0  X  0  X  X  X  0  0  0  X  0  0  X  0  X  X  X  X  X  X  X  0  X  0  0  X  0  X  X  0  0  0  X  0  X  0  0  0
 0  0  0  0  0  0  0  0  0  X  0  0  0  X  X  X  0  X  0  X  X  X  0  0  0  X  X  0  0  X  X  0  0  0  X  X  X  0  0  X  0  X  X  0  X  0  0  0  0  X  X  X  0  0  X  X  X  0  X  X  X  X  X  0  0  0  0  X  X  0  0  0  0  0  0  0  X  0  X  0  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+56x^68+44x^69+86x^70+140x^71+215x^72+224x^73+337x^74+308x^75+323x^76+402x^77+385x^78+464x^79+477x^80+492x^81+432x^82+476x^83+425x^84+426x^85+403x^86+396x^87+343x^88+328x^89+248x^90+204x^91+133x^92+118x^93+103x^94+56x^95+50x^96+12x^97+36x^98+4x^99+23x^100+2x^101+15x^102+2x^104+3x^106

The gray image is a linear code over GF(2) with n=164, k=13 and d=68.
This code was found by Heurico 1.16 in 14.6 seconds.