The generator matrix

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

generates a code of length 72 over Z4 who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+60x^57+123x^58+260x^59+422x^60+520x^61+663x^62+894x^63+989x^64+1164x^65+1393x^66+1446x^67+1616x^68+1764x^69+1868x^70+1954x^71+2066x^72+2046x^73+2049x^74+1924x^75+1704x^76+1672x^77+1456x^78+1182x^79+886x^80+716x^81+616x^82+426x^83+328x^84+200x^85+132x^86+98x^87+41x^88+46x^89+18x^90+8x^91+10x^92+4x^93+1x^94+1x^98+1x^120

The gray image is a code over GF(2) with n=144, k=15 and d=57.
This code was found by Heurico 1.10 in 119 seconds.