The generator matrix

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

generates a code of length 80 over Z4 who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+22x^67+85x^68+150x^69+220x^70+294x^71+300x^72+396x^73+396x^74+408x^75+408x^76+402x^77+434x^78+410x^79+462x^80+416x^81+464x^82+424x^83+406x^84+402x^85+311x^86+292x^87+259x^88+194x^89+171x^90+162x^91+105x^92+76x^93+47x^94+36x^95+21x^96+10x^97+5x^98+2x^101+1x^112

The gray image is a code over GF(2) with n=160, k=13 and d=67.
This code was found by Heurico 1.10 in 4.74 seconds.