The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+46x^42+152x^43+413x^44+734x^45+1428x^46+2958x^47+4634x^48+7920x^49+8702x^50+11266x^51+9137x^52+8032x^53+4651x^54+2886x^55+1199x^56+684x^57+369x^58+142x^59+86x^60+34x^61+29x^62+4x^63+18x^64+4x^65+7x^66

The gray image is a code over GF(2) with n=408, k=16 and d=168.
This code was found by Heurico 1.16 in 35.6 seconds.