The generator matrix

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

generates a code of length 55 over Z4 who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+324x^44+798x^46+1164x^48+1608x^50+2022x^52+2206x^54+2328x^56+2052x^58+1787x^60+1094x^62+587x^64+276x^66+106x^68+30x^70+1x^92

The gray image is a code over GF(2) with n=110, k=14 and d=44.
This code was found by Heurico 1.10 in 120 seconds.