The generator matrix

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

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+100x^68+14x^70+294x^72+184x^74+632x^76+508x^78+957x^80+842x^82+1208x^84+806x^86+975x^88+524x^90+554x^92+176x^94+233x^96+18x^98+114x^100+34x^104+14x^108+1x^112+2x^116+1x^120

The gray image is a linear code over GF(2) with n=168, k=13 and d=68.
This code was found by Heurico 1.16 in 16.7 seconds.