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

generates a code of length 90 over Z4 who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+44x^77+108x^78+176x^79+230x^80+274x^81+358x^82+390x^83+411x^84+380x^85+388x^86+402x^87+390x^88+450x^89+380x^90+430x^91+436x^92+386x^93+388x^94+336x^95+340x^96+310x^97+278x^98+206x^99+171x^100+166x^101+116x^102+84x^103+60x^104+28x^105+24x^106+20x^107+6x^108+8x^109+8x^110+2x^111+3x^112+2x^113+2x^115

The gray image is a code over GF(2) with n=180, k=13 and d=77.
This code was found by Heurico 1.10 in 5.45 seconds.