The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  X  X  X  X  1  1  X  X  1  1  X  0  1  1  0  X  1  X  1  1  1  X  1  1  0  1  X  1  X  1
 0  X  0  0  0  0  0  0  0  0  0  0  0  0  X  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  0  X  0  X  X  X  X  0  X  0  X  0  0  0  X  X  0  X  X  0  0  X  0  X  X  0  X  X  X  0  X  0  X  0  0  X  0  0  0  X  0  0  X  0  X  0  0  X  X  X
 0  0  X  0  0  0  0  0  0  0  0  0  0  0  X  0  0  0  0  X  X  X  X  X  X  X  0  X  0  X  0  0  0  X  X  X  0  0  0  X  0  0  0  X  0  0  X  X  0  0  X  0  X  0  0  0  X  X  X  X  0  X  0  X  0  0  X  X  X  X  0  X  0  0  0  0  0  X  X  X  X  X
 0  0  0  X  0  0  0  0  0  0  0  0  0  X  0  0  0  X  X  X  X  X  X  0  0  0  X  X  0  X  X  0  0  0  X  0  0  0  X  0  X  X  0  0  X  0  0  X  X  0  X  X  X  X  0  X  0  X  X  X  X  X  X  0  X  X  X  X  X  0  X  X  X  X  X  X  X  0  X  0  0  X
 0  0  0  0  X  0  0  0  0  0  0  0  0  X  0  X  X  X  X  X  X  0  X  X  0  X  X  0  0  0  0  X  X  X  X  0  0  0  X  X  0  0  0  0  0  0  X  X  X  X  0  0  0  X  0  X  X  X  0  0  X  0  0  X  0  X  0  X  X  0  0  0  0  X  X  0  0  X  X  0  X  0
 0  0  0  0  0  X  0  0  0  0  0  0  X  0  0  X  X  0  X  X  0  X  0  X  0  X  X  0  X  X  0  0  0  0  0  0  X  X  0  0  0  0  X  0  X  X  X  0  X  X  X  0  0  0  X  X  0  X  0  0  0  0  0  X  0  X  X  0  0  X  X  0  0  X  X  X  X  X  0  X  X  0
 0  0  0  0  0  0  X  0  0  0  0  0  X  0  0  0  X  X  X  X  0  X  X  0  X  0  X  0  0  0  0  X  X  0  0  X  X  0  0  X  X  0  0  X  X  X  X  X  X  0  X  X  X  0  0  0  0  0  X  0  0  X  X  0  X  0  X  0  0  0  0  0  X  0  X  X  0  0  0  0  0  X
 0  0  0  0  0  0  0  X  0  0  0  X  0  0  0  0  X  X  0  X  0  0  0  X  X  X  X  X  X  0  X  0  X  X  X  0  0  X  0  X  X  0  X  0  X  X  X  0  0  0  X  0  X  X  0  0  0  X  0  0  X  X  X  0  X  0  0  X  X  0  X  X  X  X  X  X  0  X  X  0  0  0
 0  0  0  0  0  0  0  0  X  0  0  X  0  0  0  X  0  0  X  0  X  0  0  X  0  0  X  0  X  X  X  0  X  X  X  0  X  X  X  0  X  X  0  X  0  X  0  X  X  X  X  X  X  0  X  0  X  0  0  0  X  0  0  X  0  X  X  0  0  X  X  0  X  0  X  0  X  0  X  0  0  0
 0  0  0  0  0  0  0  0  0  X  0  X  X  X  X  X  0  0  0  X  0  0  X  X  0  0  X  0  X  0  0  X  X  0  X  X  X  X  0  0  X  X  X  0  X  X  0  X  X  0  0  0  X  0  X  0  0  X  0  X  0  0  0  0  X  0  X  X  0  X  0  0  0  0  0  0  X  X  X  X  X  X
 0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  0  0  X  X  X  X  X  0  X  0  X  0  X  0  0  0  X  0  0  0  0  0  X  0  X  X  0  X  X  0  X  0  X  X  X  X  X  X  0  X  0  X  X  0  0  X  X  X  X  0  X  X  X  X  X  X  0  0  X  X  0  0  X  X  X  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+159x^68+2x^70+322x^72+76x^74+463x^76+242x^78+618x^80+392x^82+643x^84+230x^86+409x^88+76x^90+243x^92+6x^94+143x^96+58x^100+9x^104+2x^108+1x^112+1x^128

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 5.92 seconds.