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  8  2  0  1  8  2 12  1  1  2  1  8  8  1  1  4  8  1  2  1  8  1  1  1  1  1  1  1  1  1
 0  2  0  2  0  0  2  6  4 10  4  6 14  0  8 10  6 12  6  8 14 12  2 14  2  6  2  4  2  0  2  4  8  2  0  6 10  2  2  6  2 12  2  6 10 10 12 12 12 12  8  0
 0  0  2  2  0  6  2  4  0  2  2  8 10  0 10  4 14 12  4  2  8  2 10  2  4  8  6  6  0  0 10  2  8  2  2  4 12  0 12 10  6  6  6 14  6  8  8  6 12  8  6  0
 0  0  0  4  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8 12  4  4  4 12 12 12  0  4  0  4  4 12  4  8  4 12 12  0  4 12 12  0  0  8 12  8  8  8 12  8  0  0
 0  0  0  0 12  0  0  0  0  0 12 12  4 12  4 12 12  0  8 12  8 12  4  0  4  4  8  8  4 12  4  8  8 12  4  4 12  4 12 12  4 12  4  4 12  0 12  8 12  4  8  0
 0  0  0  0  0 12  8 12  4 12 12 12  0  4  0  8 12  8  8  8  8  4  8 12  4  8 12  0 12  0  4  4  4  4  0  0 12  8 12  0  0  0  8  0  4  4  0  8 12  4  4  8

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

Homogenous weight enumerator: w(x)=1x^0+35x^42+142x^43+328x^44+662x^45+1018x^46+1720x^47+2978x^48+4270x^49+6621x^50+9520x^51+10705x^52+9624x^53+6977x^54+4532x^55+2742x^56+1528x^57+939x^58+546x^59+307x^60+162x^61+81x^62+52x^63+26x^64+10x^65+8x^66+1x^72+1x^74

The gray image is a code over GF(2) with n=416, k=16 and d=168.
This code was found by Heurico 1.16 in 55.3 seconds.