The generator matrix

 1  0  0  0  0  1  1  1  0  1  1  2  1  1  0  0  1  1  2  1  1  0  2  1  1  2  2  2  1  2  1  1  2  1  1  1  1  1  2  2  1  1  1  2  1  1  0  2  0  1  1  0  1  2
 0  1  0  0  0  0  0  0  0  1  1  1  1  1  1  1  3  2  2  3  0  2  0  0  3  1  1  1  1  1  3  3  0  2  2  3  3  0  2  0  3  3  3  2  3  0  1  2  1  3  3  2  1  1
 0  0  1  0  0  0  1  1  1  0  2  0  1  3  1  1  0  1  1  2  1  1  0  2  1  3  2  1  1  0  0  1  0  3  2  1  1  1  0  1  2  2  3  1  1  3  2  1  0  2  2  0  0  3
 0  0  0  1  0  1  1  0  1  1  0  3  2  3  2  1  2  0  1  1  3  2  0  3  0  1  1  2  3  2  2  1  1  2  1  3  3  3  1  0  2  3  1  3  3  1  3  1  1  3  1  1  1  2
 0  0  0  0  1  1  0  1  1  2  3  3  0  1  3  0  3  1  3  0  2  2  1  3  0  0  3  1  1  0  2  1  0  0  2  2  2  3  1  1  0  1  2  3  2  3  0  3  2  3  0  1  0  2
 0  0  0  0  0  2  0  0  0  0  0  0  2  0  0  2  2  2  2  2  0  0  2  2  0  0  2  0  2  2  0  2  2  0  0  2  0  2  2  0  2  2  2  0  0  0  0  0  2  0  2  0  2  2
 0  0  0  0  0  0  2  0  2  2  0  2  2  2  0  0  2  2  0  0  2  0  2  0  0  2  0  0  0  0  2  2  2  2  0  2  0  2  2  2  0  2  2  0  2  2  0  0  2  0  2  2  0  0
 0  0  0  0  0  0  0  2  2  0  2  2  2  2  0  0  0  0  2  0  2  2  0  2  0  2  0  2  2  0  2  2  2  0  0  0  2  0  0  2  2  2  2  2  0  0  2  0  0  0  2  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+228x^44+566x^46+779x^48+932x^50+1054x^52+1052x^54+1130x^56+946x^58+810x^60+400x^62+190x^64+66x^66+28x^68+6x^70+3x^72+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 7.93 seconds.