The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+109x^44+88x^46+413x^48+278x^50+599x^52+552x^54+711x^56+404x^58+437x^60+208x^62+210x^64+6x^66+53x^68+25x^72+2x^76

The gray image is a code over GF(2) with n=110, k=12 and d=44.
This code was found by Heurico 1.16 in 2.45 seconds.