The generator matrix

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

generates a code of length 54 over Z4 who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+78x^42+298x^44+484x^46+777x^48+902x^50+1033x^52+1046x^54+1105x^56+896x^58+722x^60+454x^62+240x^64+100x^66+43x^68+8x^70+5x^72

The gray image is a code over GF(2) with n=108, k=13 and d=42.
This code was found by Heurico 1.10 in 2.81 seconds.