The generator matrix

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

generates a code of length 66 over Z4 who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+268x^54+706x^56+1086x^58+1414x^60+1746x^62+1932x^64+2048x^66+2022x^68+1702x^70+1423x^72+1108x^74+620x^76+228x^78+73x^80+6x^82+1x^120

The gray image is a code over GF(2) with n=132, k=14 and d=54.
This code was found by Heurico 1.10 in 14.5 seconds.