The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+338x^44+750x^46+1238x^48+1554x^50+2005x^52+2228x^54+2395x^56+1998x^58+1732x^60+1142x^62+630x^64+238x^66+101x^68+24x^70+6x^72+2x^74+1x^80+1x^88

The gray image is a code over GF(2) with n=110, k=14 and d=44.
This code was found by Heurico 1.16 in 85.5 seconds.