The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+89x^42+132x^43+288x^44+328x^45+474x^46+590x^47+674x^48+794x^49+928x^50+1090x^51+1056x^52+1160x^53+1089x^54+1228x^55+1121x^56+1058x^57+956x^58+820x^59+721x^60+522x^61+479x^62+270x^63+215x^64+148x^65+79x^66+30x^67+19x^68+22x^69+2x^70+1x^96

The gray image is a code over GF(2) with n=108, k=14 and d=42.
This code was found by Heurico 1.10 in 10.9 seconds.