The generator matrix

 1  0  0  0  1  1  1  2 10  1 12  1  1  1 14 12 14  0  1  6  1  1  0  2  1 12  2  1  1 14  1  1  2 10  1  8  2  8  1  6  1  1  6  1 12  1  1  1  1  1  1
 0  1  0  0  0  9  5  1  1  8  1  4  7 11  0  1 10 10  2  1 10  5  1 12  1  4  1 10  9  1 10 11  1  1 10 14  1  2  6 14  3  9 12  7  1 11  4  0  6  4  0
 0  0  1  0  1  1  4  5  2 10  3  3 12  5  1  5  1 14  3 10 14  7  8  1 14  1  7  0  2 12 11 12  9  6 15  0 15  1  2  1  6  5  1 13  5  9  0  6  9 11  4
 0  0  0  1  1  4  1  1 15  9  6 10 14 11  9  5  3  1  1 10  7 11 11 15 13 10 12  4  0  4 10  7 12  9  0  1  7 14  6 13  4  1  2 12  6  8  9  8 10  1  6
 0  0  0  0 12  0  0  0  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  4 12 12 12 12 12  4 12  4 12  4  4  4  8 12  4  4  8  4  8  4 12  4  8  8 12 12

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

Homogenous weight enumerator: w(x)=1x^0+146x^43+867x^44+2714x^45+6161x^46+11982x^47+20056x^48+29860x^49+37877x^50+41724x^51+39222x^52+29898x^53+20504x^54+12004x^55+5381x^56+2402x^57+877x^58+292x^59+105x^60+36x^61+17x^62+10x^63+2x^65+4x^66+2x^67

The gray image is a code over GF(2) with n=408, k=18 and d=172.
This code was found by Heurico 1.16 in 475 seconds.