The generator matrix

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

generates a code of length 84 over Z4 who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+62x^68+86x^69+269x^70+320x^71+524x^72+616x^73+749x^74+814x^75+1004x^76+1276x^77+1411x^78+1422x^79+1528x^80+1764x^81+1691x^82+1820x^83+1769x^84+1900x^85+1817x^86+1812x^87+1698x^88+1660x^89+1360x^90+1158x^91+1026x^92+830x^93+617x^94+454x^95+463x^96+260x^97+231x^98+112x^99+95x^100+50x^101+38x^102+24x^103+18x^104+4x^105+9x^106+4x^108+2x^109

The gray image is a code over GF(2) with n=168, k=15 and d=68.
This code was found by Heurico 1.10 in 151 seconds.