The generator matrix

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

generates a code of length 54 over Z4 who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+237x^44+536x^46+803x^48+920x^50+1024x^52+1136x^54+1130x^56+980x^58+647x^60+436x^62+234x^64+84x^66+19x^68+4x^70+1x^84

The gray image is a code over GF(2) with n=108, k=13 and d=44.
This code was found by Heurico 1.10 in 3 seconds.