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

generates a code of length 54 over Z4 who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+257x^44+472x^46+914x^48+858x^50+1023x^52+1106x^54+1112x^56+924x^58+794x^60+436x^62+225x^64+42x^66+21x^68+2x^70+4x^72+1x^92

The gray image is a code over GF(2) with n=108, k=13 and d=44.
This code was found by Heurico 1.16 in 50.7 seconds.