The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+216x^42+541x^44+4x^45+820x^46+200x^47+1644x^48+1684x^49+3920x^50+4248x^51+6158x^52+4268x^53+4015x^54+1688x^55+1673x^56+188x^57+775x^58+8x^59+424x^60+225x^62+54x^64+13x^66+1x^84

The gray image is a code over GF(2) with n=416, k=15 and d=168.
This code was found by Heurico 1.16 in 20.9 seconds.