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

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

Homogenous weight enumerator: w(x)=1x^0+70x^43+300x^44+614x^45+1093x^46+1586x^47+2261x^48+3718x^49+4539x^50+4566x^51+4626x^52+3522x^53+2279x^54+1654x^55+899x^56+490x^57+271x^58+124x^59+101x^60+32x^61+8x^62+3x^64+8x^65+2x^66+1x^68

The gray image is a code over GF(2) with n=408, k=15 and d=172.
This code was found by Heurico 1.16 in 13.3 seconds.