The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+238x^44+558x^46+791x^48+900x^50+1021x^52+1152x^54+1127x^56+896x^58+738x^60+458x^62+224x^64+68x^66+19x^68+1x^88

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 7.94 seconds.