The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+204x^42+547x^44+774x^46+884x^48+1133x^50+1159x^52+1112x^54+901x^56+786x^58+409x^60+191x^62+61x^64+21x^66+5x^68+2x^70+1x^72+1x^78

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 7.56 seconds.