The generator matrix

 1  0  1  1  1  4  1  1  6  1  1  4 10  1  1  1  1 12  8  1  1  1  8  1  1  1 14  1  1  1  1  0  2  0  1  2  2  1  1  4  4  1  1  1  1  2  0  0  1  2  1
 0  1  1  0  3  1  5  4  1  8  3  1  1 10 15  9 10  1  1  8  1 14  1 11  8  2  1  1  6 12 11  1  1  1  1  6  6  1  3  1  1  4  8  6 15 14  1 12  3 14  0
 0  0  2  0  0  0  2 10  6  2  8 14  0  8  2  4  6 14  2  8 12 14 12 10 14  4 10 14  0 14  2  0 12  6  2 14  6  4 12 12 14  2  8 10 14  4 10  2  2  6  0
 0  0  0  2  0  2  2  8 14 14  6  4  6 14 10  2  6  0 14 12  0 12  8  8 12 14  0  4  6  6  4 14 12  6  6  6  8 14  0  4  2 12 14  6  2  2  0 10  2  2  0
 0  0  0  0  8  0  0  8  8  8  8  8  0  0  0  8  8  8  8  0  0  0  8  0  0  8  0  8  8  0  0  8  0  0  8  0  8  0  0  8  8  8  0  0  8  0  0  0  8  8  0
 0  0  0  0  0  8  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  0  0  8  8  0  8  8  8  0  8  0  8  0  8  8  0  0  0  0  0  8  0  8  0  8  8  0  8  0  8

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

Homogenous weight enumerator: w(x)=1x^0+70x^43+371x^44+862x^45+1623x^46+2914x^47+5159x^48+6716x^49+10152x^50+10048x^51+9868x^52+6898x^53+5162x^54+2850x^55+1488x^56+734x^57+392x^58+110x^59+65x^60+18x^61+15x^62+8x^63+8x^64+2x^65+2x^69

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 35.1 seconds.