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

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

Homogenous weight enumerator: w(x)=1x^0+204x^42+168x^43+995x^44+764x^45+2268x^46+2256x^47+6013x^48+5404x^49+10854x^50+7400x^51+11258x^52+5372x^53+6062x^54+2336x^55+2258x^56+708x^57+682x^58+128x^59+251x^60+40x^61+86x^62+24x^64+4x^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 55.2 seconds.