The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+150x^44+318x^46+724x^48+802x^50+1083x^52+988x^54+1147x^56+1008x^58+848x^60+594x^62+344x^64+126x^66+47x^68+4x^70+7x^72+1x^96

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 7.78 seconds.