The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+137x^44+186x^46+447x^48+442x^50+634x^52+520x^54+553x^56+440x^58+366x^60+174x^62+132x^64+30x^66+30x^68+3x^72+1x^76

The gray image is a code over GF(2) with n=108, k=12 and d=44.
This code was found by Heurico 1.16 in 2.05 seconds.