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

generates a code of length 51 over Z16 who´s minimum homogenous weight is 43.

Homogenous weight enumerator: w(x)=1x^0+288x^43+642x^44+1264x^45+1838x^46+2840x^47+4917x^48+6520x^49+9224x^50+9848x^51+10114x^52+6692x^53+4710x^54+2866x^55+1693x^56+1082x^57+486x^58+272x^59+132x^60+56x^61+28x^62+10x^63+4x^64+2x^65+2x^66+4x^67+1x^72

The gray image is a code over GF(2) with n=408, k=16 and d=172.
This code was found by Heurico 1.16 in 51.5 seconds.