The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  1  2  1  1  1  1  1  1  4  1  2  1  0  1  1  1  4  1  1  1  0  2  1  1  1  1  2  2  2  1
 0 12  0 12  0 12  0 12  0  4  8  0 12 12  4  0  8  0  8  0 12 12  0 12 12 12  0  8  8  8 12  0 12 12  4 12  4  4 12  8  4  8  4 12 12  8 12 12 12 12 12  0
 0  0  8  0  0  0  0  0  0  0  8  8  0  8  8  0  8  0  8  8  0  0  8  8  0  0  0  8  0  8  0  8  0  8  0  0  8  0  8  8  8  8  0  8  8  8  0  8  8  8  0  0
 0  0  0  8  0  0  0  0  0  8  0  0  0  8  8  0  0  8  8  8  0  8  8  0  8  0  0  8  8  0  8  0  0  8  8  0  8  0  8  0  0  0  0  0  8  8  8  8  0  0  8  0
 0  0  0  0  8  0  0  0  0  0  0  8  0  0  0  8  0  8  8  8  0  8  0  8  8  8  8  0  0  8  0  8  0  0  8  8  8  0  0  8  0  0  8  8  8  0  8  8  8  8  0  0
 0  0  0  0  0  8  0  0  0  0  0  0  8  8  8  0  0  0  0  0  0  8  0  8  8  0  8  8  8  8  8  8  8  8  0  0  8  0  0  0  0  8  0  8  0  0  0  8  0  8  8  0
 0  0  0  0  0  0  8  0  0  0  0  8  0  0  0  8  8  8  8  0  8  0  8  0  8  8  0  8  8  0  8  8  0  8  8  0  0  8  8  8  8  0  0  0  0  8  0  8  0  8  0  8
 0  0  0  0  0  0  0  8  0  8  0  0  8  8  0  8  8  8  0  0  8  8  0  8  0  0  0  8  0  8  8  8  0  0  0  8  0  0  8  0  0  8  8  0  0  8  0  8  0  0  0  8
 0  0  0  0  0  0  0  0  8  0  8  8  8  0  8  8  8  0  0  0  8  0  0  0  0  8  8  8  0  8  8  0  0  8  8  8  8  8  0  0  0  8  8  8  0  8  0  8  8  8  0  0

generates a code of length 52 over Z16 who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+33x^42+123x^44+212x^46+439x^48+1816x^50+2997x^52+1798x^54+413x^56+197x^58+97x^60+28x^62+17x^64+10x^66+7x^68+2x^70+1x^72+1x^80

The gray image is a code over GF(2) with n=416, k=13 and d=168.
This code was found by Heurico 1.16 in 1.55 seconds.