The generator matrix

 1  0  1  1  1  0  1  1  0  1  1  2  1  1  0  0  1  1  1  1  0  2  1  1  1  1  0  1  2  1  1  1  0  1  2  1  1  1  1  1  1  0  0  1  1  1  0  2  1  2  1  1  2  1  1  1  1  2  2  1  1  0  1  0  0  1  1  1  1  1  0  1  1  2  0  1  0  1  2  1  2  0  1  1
 0  1  1  0  1  1  0  1  1  0  1  1  2  3  1  1  0  3  0  3  1  1  0  3  2  3  1  0  1  3  0  3  1  0  1  3  3  1  1  2  1  1  1  0  0  0  1  1  3  1  0  3  1  1  1  2  2  1  1  3  1  1  2  1  1  3  0  2  1  2  1  2  0  1  2  2  1  1  1  0  1  1  0  0
 0  0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  0  2  0  2  2  0  2  0  0  2  2  0  2  0  2  2  2  2  2  2  0  0  2  0  2  2  2  0  2  0  0  0  2  0  2  2  0  2  2  0  2  2  2  0  0  0  0  2  2  0  2  0  0
 0  0  0  2  0  0  0  0  0  0  0  0  2  0  0  0  0  2  0  2  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  0  2  2  2  2  0  2  0  0  2  2  0  2  2  0  0  2  0  0  2  0  2  0  2  2  2  2  0  2  0  0  2  2  2  2  0  0  2  0  0  0  0  0  0  2  2  0  0  0
 0  0  0  0  2  0  0  0  0  0  0  0  0  2  0  2  2  2  2  0  0  2  2  0  2  2  2  0  0  2  0  2  0  0  2  0  0  2  2  0  2  0  0  0  2  0  2  0  2  0  2  0  0  0  2  2  2  2  0  0  2  0  2  0  2  0  2  2  2  0  0  2  0  2  2  0  0  2  0  0  2  0  0  0
 0  0  0  0  0  2  0  0  0  0  0  2  0  0  0  2  2  2  0  2  2  0  2  2  0  0  0  2  0  0  2  2  2  0  0  2  2  0  0  0  2  0  0  2  0  0  0  2  2  2  0  2  0  2  0  0  2  0  2  2  2  0  2  0  0  0  2  2  0  2  2  0  0  2  0  0  2  2  0  0  2  2  0  0
 0  0  0  0  0  0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  0  2  0  2  2  2  2  0  2  2  0  0  0  2  0  0  2  2  2  2  0  2  0  0  2  2  2  0  2  0  2  2  0  0  2  0  2  2  2  2  2  0  2  0  0  2  0  2  2  0  0  2  0  2  2  0  0  0  0
 0  0  0  0  0  0  0  2  0  0  0  0  0  2  2  0  2  2  2  0  2  0  2  0  2  2  2  2  2  0  0  0  2  0  2  2  2  0  0  2  0  0  0  2  2  0  0  0  0  2  2  0  0  0  0  0  0  2  0  2  0  2  2  0  0  0  2  2  0  2  2  2  0  2  0  2  2  0  0  0  2  2  2  2
 0  0  0  0  0  0  0  0  2  0  0  2  0  0  2  0  0  2  2  2  0  2  2  0  2  0  0  2  0  2  2  0  2  2  2  2  0  0  0  2  0  2  2  2  0  0  0  2  2  2  2  0  2  2  2  2  2  0  2  0  2  2  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  0  2  2  2
 0  0  0  0  0  0  0  0  0  2  0  0  2  0  2  2  2  2  0  0  2  2  2  0  0  2  0  0  2  2  2  2  2  2  0  0  0  0  0  2  2  0  2  0  0  2  0  2  0  2  2  0  2  2  2  0  2  2  2  2  0  0  2  0  2  0  2  0  2  0  0  2  0  2  2  0  2  2  0  2  2  2  0  0
 0  0  0  0  0  0  0  0  0  0  2  0  0  2  2  2  0  2  0  2  2  2  0  2  0  0  2  0  0  2  2  0  0  0  2  2  0  2  0  2  2  0  2  2  2  0  2  0  0  0  0  0  2  2  2  2  0  2  0  0  2  2  0  2  0  0  0  2  0  0  2  2  0  2  0  2  2  0  0  2  2  2  2  2

generates a code of length 84 over Z4 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 code over GF(2) with n=168, k=13 and d=68.
This code was found by Heurico 1.16 in 16.9 seconds.