The generator matrix

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

generates a code of length 52 over Z16 who´s minimum homogenous weight is 43.

Homogenous weight enumerator: w(x)=1x^0+92x^43+340x^44+684x^45+1134x^46+1980x^47+2886x^48+4854x^49+6315x^50+10210x^51+8364x^52+10416x^53+6360x^54+5086x^55+2882x^56+1744x^57+1035x^58+588x^59+288x^60+150x^61+65x^62+26x^63+19x^64+6x^65+2x^66+2x^67+4x^68+2x^69+1x^70

The gray image is a code over GF(2) with n=416, k=16 and d=172.
This code was found by Heurico 1.16 in 52.4 seconds.