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  4  2  1  8  0  8  2  1  1  1  1  2  0  2  2  0  8 12  4  1  0  2  1  2  1  2 12  2  1
 0  2  0  0  0  2  6 14 12  4 14  2 12  8  6 10  2  8  2  6  8 12  4  8  8  2  2 12 14 10 14 14  8  6 12  4  8  8  2  4  2  2 12  2  0 14  4 12  2  8  0
 0  0  2  0  2  2  2  0  8 10  2  4  4  6  0 14  4  8  2 14  8 10  2  4  6 14  4  2 10  2 10  8 12 10  2  0 10  2 12  8  4  4  2 14  4  8  6  2  0 12  0
 0  0  0  2  2  0  2  2 14  6 12  8  4 12 14  6 10 12 12 14  6  0  0  6 10  2 10  6 14  2  8  0  0  4  4 14  6  2 14  2 12  6  6  4  2  6 14  2  0 14  0
 0  0  0  0  8  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  8  8  8  8  8  0  8  8  8  8  8  0  0  8  8  0  8  8  0
 0  0  0  0  0  8  0  0  0  0  0  8  8  8  8  0  0  0  0  8  8  0  8  8  8  8  0  8  0  8  8  0  0  8  8  0  0  8  8  8  8  0  8  0  0  0  0  0  0  8  8
 0  0  0  0  0  0  8  8  8  8  0  0  0  0  8  0  0  8  8  0  0  8  0  0  8  0  8  0  0  8  8  0  8  0  8  0  0  8  8  0  8  8  8  8  0  0  8  0  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+87x^42+350x^43+682x^44+1276x^45+1818x^46+3452x^47+4356x^48+7840x^49+7376x^50+10844x^51+7509x^52+8124x^53+4324x^54+3520x^55+1750x^56+1116x^57+575x^58+262x^59+151x^60+72x^61+26x^62+4x^63+13x^64+4x^65+2x^66+1x^68+1x^76

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 50.5 seconds.