The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+275x^46+16x^47+482x^48+256x^49+822x^50+480x^51+762x^52+256x^53+498x^54+16x^55+156x^56+52x^58+5x^60+11x^62+1x^64+6x^66+1x^76

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 65 seconds.