The generator matrix

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

generates a code of length 89 over Z4 who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+59x^80+112x^81+108x^82+172x^83+158x^84+138x^85+122x^86+106x^87+143x^88+92x^89+87x^90+108x^91+105x^92+66x^93+47x^94+68x^95+57x^96+60x^97+49x^98+30x^99+31x^100+34x^101+27x^102+18x^103+14x^104+8x^105+8x^106+8x^107+6x^108+2x^109+2x^112+2x^115

The gray image is a code over GF(2) with n=178, k=11 and d=80.
This code was found by Heurico 1.10 in 0.297 seconds.