The generator matrix

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

generates a code of length 66 over Z4 who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+96x^56+352x^58+483x^60+472x^62+493x^64+462x^66+468x^68+420x^70+344x^72+256x^74+127x^76+68x^78+34x^80+18x^82+2x^84

The gray image is a code over GF(2) with n=132, k=12 and d=56.
This code was found by Heurico 1.10 in 0.828 seconds.