The generator matrix

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

generates a code of length 51 over Z16 who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+144x^42+32x^43+476x^44+352x^45+1156x^46+1308x^47+2726x^48+3376x^49+4788x^50+4224x^51+4747x^52+3284x^53+2676x^54+1436x^55+1057x^56+280x^57+414x^58+40x^59+157x^60+4x^61+68x^62+16x^64+2x^66+4x^68

The gray image is a code over GF(2) with n=408, k=15 and d=168.
This code was found by Heurico 1.16 in 16.2 seconds.