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

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

Homogenous weight enumerator: w(x)=1x^0+98x^46+212x^47+472x^48+416x^49+514x^50+748x^51+625x^52+356x^53+340x^54+104x^55+66x^56+68x^57+42x^58+8x^59+9x^60+8x^61+6x^62+2x^64+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 0.339 seconds.