The generator matrix

 1  0  1  1  1  0  1  1  0  1  1  2  1  1  0  1  0  1  1  0  1  1  1  0  2  1  1  1  1  0  0  1  2  1  1  2  0  1  2  1  1  1  1  1  2  2  1  2  1  0  1  0  1  1
 0  1  1  0  1  1  0  1  1  0  3  1  2  3  1  0  1  3  2  1  0  3  3  1  1  3  0  2  1  1  1  3  1  1  0  1  1  1  1  0  1  1  1  0  1  1  3  1  0  2  0  0  3  0
 0  0  2  0  0  0  0  0  0  0  2  0  0  0  0  0  2  2  0  2  2  0  2  2  2  0  2  0  0  2  0  0  0  0  2  2  2  2  0  0  2  2  0  0  0  2  0  2  0  2  0  0  2  2
 0  0  0  2  0  0  0  0  0  0  0  0  2  0  0  0  0  2  2  2  0  2  2  2  2  2  2  2  0  2  2  2  0  2  0  2  0  2  0  2  0  2  2  0  0  0  2  0  2  2  0  2  2  0
 0  0  0  0  2  0  0  0  0  0  2  0  0  0  2  0  2  2  0  0  0  2  0  0  2  0  2  2  0  2  2  0  2  0  2  0  2  0  2  2  2  0  0  2  2  0  2  2  2  0  0  0  2  2
 0  0  0  0  0  2  0  0  0  0  0  2  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  0  2  2  2  2  0  2  2  0  2  2  2  2  0  0  2
 0  0  0  0  0  0  2  0  0  0  0  0  0  2  0  0  2  0  2  0  2  2  2  0  0  2  2  2  2  0  0  2  0  0  0  2  0  0  2  2  0  0  2  2  2  2  0  2  0  2  0  2  0  0
 0  0  0  0  0  0  0  2  0  0  2  0  0  0  2  2  2  0  2  0  2  0  0  2  0  0  0  2  2  2  0  0  0  2  2  2  2  0  2  2  0  2  0  2  0  0  2  0  0  2  0  2  2  2
 0  0  0  0  0  0  0  0  2  0  0  2  0  2  2  0  2  2  0  2  0  2  2  0  0  0  0  0  2  2  0  2  2  0  0  0  0  2  0  2  2  0  0  2  2  2  0  0  0  0  2  2  2  0
 0  0  0  0  0  0  0  0  0  2  0  0  2  2  2  2  0  0  2  2  2  2  0  2  0  2  2  0  0  2  2  0  0  0  2  2  2  2  0  0  0  0  0  2  2  0  0  2  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+197x^44+116x^46+467x^48+384x^50+643x^52+544x^54+614x^56+376x^58+442x^60+108x^62+142x^64+8x^66+43x^68+8x^72+3x^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 23.7 seconds.