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  3  3  0  1  2  1  3  0  3  2  0  3  2  2  3  0  1  0  1  1  3  2  2  1  1  1  2  3  2  3  2  1  0  2  2  2  3  3  3  1  3  0  1  2  0
 0  0  0  0  1  0  1  1  0  3  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  0  1  1  2  3  1  0  2  2  2  3  3  1  1  3  1  2  0  2  1  1  1  0  3  1  2  1  3  0  3  3  0  3  1  2  2  2  3  3  1  3  0  2  2  3  3  2  0  0  3  0
 0  0  0  0  0  0  2  0  2  2  0  0  0  0  2  2  2  2  2  2  0  0  0  2  2  2  2  0  0  2  0  0  2  0  0  2  0  0  2  2  2  0  0  0  0  0  2  0  2  0  2  0  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+78x^44+124x^45+230x^46+266x^47+329x^48+392x^49+407x^50+452x^51+452x^52+524x^53+583x^54+594x^55+490x^56+522x^57+507x^58+496x^59+424x^60+364x^61+299x^62+206x^63+178x^64+108x^65+77x^66+28x^67+30x^68+12x^69+6x^70+6x^71+2x^72+2x^73+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 1.16 in 7.67 seconds.