The generator matrix

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

generates a code of length 66 over Z4 who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+42x^52+286x^54+755x^56+956x^58+1400x^60+1758x^62+1931x^64+2086x^66+2072x^68+1688x^70+1429x^72+966x^74+590x^76+292x^78+91x^80+32x^82+8x^84+1x^112

The gray image is a code over GF(2) with n=132, k=14 and d=52.
This code was found by Heurico 1.10 in 13.9 seconds.