The generator matrix

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

generates a code of length 85 over Z4 who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+105x^68+150x^69+390x^70+512x^71+747x^72+878x^73+1199x^74+1400x^75+1743x^76+1908x^77+2177x^78+2538x^79+2851x^80+3140x^81+3347x^82+3720x^83+3610x^84+3838x^85+3718x^86+3984x^87+3656x^88+3370x^89+3043x^90+2764x^91+2306x^92+1938x^93+1713x^94+1314x^95+1027x^96+720x^97+623x^98+312x^99+257x^100+148x^101+138x^102+84x^103+69x^104+36x^105+27x^106+12x^107+11x^108+2x^109+8x^110+1x^112+1x^122

The gray image is a code over GF(2) with n=170, k=16 and d=68.
This code was found by Heurico 1.10 in 646 seconds.