The generator matrix

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

generates a code of length 80 over Z4 who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+73x^68+154x^69+231x^70+294x^71+325x^72+352x^73+367x^74+388x^75+453x^76+420x^77+416x^78+486x^79+497x^80+476x^81+398x^82+416x^83+386x^84+338x^85+295x^86+316x^87+298x^88+224x^89+153x^90+124x^91+119x^92+80x^93+56x^94+22x^95+22x^96+4x^97+2x^98+1x^100+2x^102+2x^103+1x^104

The gray image is a code over GF(2) with n=160, k=13 and d=68.
This code was found by Heurico 1.10 in 4.81 seconds.