The generator matrix

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

generates a code of length 55 over Z4 who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+38x^42+94x^43+181x^44+264x^45+389x^46+480x^47+564x^48+668x^49+786x^50+880x^51+1008x^52+1108x^53+1077x^54+1204x^55+1133x^56+1084x^57+1061x^58+992x^59+840x^60+638x^61+570x^62+412x^63+328x^64+230x^65+157x^66+88x^67+39x^68+38x^69+14x^70+8x^71+2x^72+2x^73+2x^74+2x^75+2x^78

The gray image is a code over GF(2) with n=110, k=14 and d=42.
This code was found by Heurico 1.10 in 10.9 seconds.