The generator matrix

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

generates a code of length 51 over Z16 who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+239x^46+96x^47+375x^48+504x^49+474x^50+848x^51+399x^52+512x^53+353x^54+80x^55+99x^56+8x^57+71x^58+21x^60+12x^62+3x^66+1x^80

The gray image is a code over GF(2) with n=408, k=12 and d=184.
This code was found by Heurico 1.16 in 74.6 seconds.