The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+96x^44+104x^45+194x^46+298x^47+340x^48+388x^49+416x^50+452x^51+465x^52+526x^53+524x^54+578x^55+574x^56+532x^57+461x^58+472x^59+432x^60+384x^61+297x^62+206x^63+177x^64+104x^65+82x^66+36x^67+23x^68+10x^69+7x^70+6x^71+4x^72+1x^74+1x^78+1x^86

The gray image is a code over GF(2) with n=110, k=13 and d=44.
This code was found by Heurico 1.10 in 2.94 seconds.