The generator matrix

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

generates a code of length 52 over Z4 who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+184x^42+550x^44+808x^46+921x^48+1096x^50+1123x^52+1065x^54+1018x^56+721x^58+423x^60+187x^62+55x^64+35x^66+4x^68+1x^72

The gray image is a code over GF(2) with n=104, k=13 and d=42.
This code was found by Heurico 1.16 in 7.29 seconds.