The generator matrix

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

generates a code of length 55 over Z4 who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+177x^46+419x^48+431x^50+541x^52+536x^54+500x^56+528x^58+384x^60+305x^62+182x^64+63x^66+17x^68+6x^70+2x^72+2x^74+2x^76

The gray image is a code over GF(2) with n=110, k=12 and d=46.
This code was found by Heurico 1.16 in 22.5 seconds.