The generator matrix

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

generates a code of length 64 over Z4 who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+221x^52+660x^54+1106x^56+1410x^58+1732x^60+2046x^62+2142x^64+1926x^66+1743x^68+1538x^70+982x^72+528x^74+247x^76+84x^78+17x^80+1x^108

The gray image is a code over GF(2) with n=128, k=14 and d=52.
This code was found by Heurico 1.10 in 13.8 seconds.