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  X  X  X  X  X  X  X  X  1  X  X  1  0  X  0  1  1  0  1  0  1  1  1  1  X  0  1  1  X  1  1  X  1  X  1  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  0  X  X  X  X  0  X  0  0  0  X  X  X  0  X  X  X  0  0  X  0  X  X  0  0  X  0  X  X  0  X  0  0  0  X  X  X  X  0  X  X  X  X  0  0  X  0  0  X  X  0  0  0
 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  0  0  X  0  0  0  X  X  X  0  0  0  X  X  X  0  X  X  0  0  X  X  X  X  0  0  0  0  0  X  0  0  0  X  0  X  X  X  0  0  X  0  0  X  X  X  X  X  0  0  X  0  X  X  0  0  0
 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  0  X  0  X  X  X  0  X  0  0  X  X  0  0  0  X  X  X  0  X  0  X  X  0  X  X  X  0  X  X  X  0  X  0  0  0  X  0  X  0  X  0  0  X  0  0  X  0  X  0  0  0  0  0  0  0  0  0
 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  X  0  0  0  X  X  X  X  X  0  X  X  0  0  0  X  0  0  0  0  X  0  0  0  0  0  X  X  0  X  0  0  0  0  0  0  X  0  X  X  X  0  X  X  X  X  0  X  X  X  X  X  X  0  X  0  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  X  X  0  0  X  X  0  0  0  X  0  X  0  0  0  0  X  X  0  X  X  X  X  X  0  0  0  0  X  0  X  0  X  X  0  0  X  0  0  0  0  0  X  X  X  X  X  0  X  0  X  X  0  X  X  X  X
 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  X  0  0  X  X  X  0  0  0  0  X  0  0  0  X  X  X  X  0  X  0  0  0  X  0  X  X  0  0  X  0  0  0  X  X  0  X  0  0  X  X  0  X  X  0  0  0  X  X  X  0  0  0  X  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  0  0  X  0  X  X  X  X  0  0  0  X  X  X  X  X  0  0  0  0  X  X  X  X  X  0  X  X  0  X  X  0  X  0  X  0  X  X  0  X  X  X  0  X  0  X  0  X  X  X  0  0  0  X  X  X  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  0  0  X  X  X  0  0  X  X  0  X  X  X  X  0  0  0  X  X  X  X  0  X  0  X  X  X  X  X  X  X  X  X  X  0  X  X  X  0  0  0  X  0  X  0  X  X  X  0  0  X  0  X  0  X  X  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  X  0  0  X  X  0  X  X  0  0  0  0  X  0  0  0  X  0  X  0  X  X  X  0  0  X  0  0  0  X  0  0  X  X  0  X  0  X  0  X  0  0  0  X  X  0  X  X  X  X  X  0  0  0  0
 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  0  0  0  0  X  0  X  0  0  X  0  X  X  0  0  0  X  0  0  X  0  0  X  0  0  X  X  X  0  X  X  X  0  X  X  0  0  X  X  X  0  X  X  0  X  X  0  0  X  X  X  0  0  X  X  0  0

generates a code of length 84 over Z2[X]/(X^2) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+64x^68+245x^72+30x^74+399x^76+164x^78+535x^80+310x^82+679x^84+344x^86+501x^88+138x^90+321x^92+36x^94+179x^96+2x^98+93x^100+42x^104+12x^108+1x^128

The gray image is a linear code over GF(2) with n=168, k=12 and d=68.
This code was found by Heurico 1.16 in 5.9 seconds.