The generator matrix

 1  0  1  1  1  6  1  1 12  1  1 10  1  1  0  1  1  6  1  1 12  1  1  6 10  1  1 12  1  1  1  1 10  1  1  0  1  1  0 10  1  1  1  1  0  6  8 12 12  2  2
 0  1  3  6  5  1 12 15  1  9 10  1  0  3  1  6  5  1 12 15  1 10  9  1  1  3  6  1 14  5 15  0  1 12  5  1 10 12  1  1  9  5  3  6  1  1  1  1  1  0 12
 0  0  8  0  0  0  0  0  8  8  0  8  8  8  0  8  8  0  0  0  0  8  8  8  8  0  0  8  8  0  8  8  0  8  0  8  8  0  0  8  0  0  8  0  0  8  8  8  0  8  0
 0  0  0  8  0  0  8  0  8  8  8  0  8  8  0  0  0  8  0  8  8  0  8  8  0  8  0  0  8  0  0  8  8  0  8  8  8  0  0  8  0  8  0  0  8  8  0  8  8  8  8
 0  0  0  0  8  0  8  8  0  0  8  0  0  8  8  0  8  8  0  8  0  8  0  8  8  0  8  0  8  0  8  8  8  0  0  8  8  8  0  0  8  8  8  0  8  8  8  8  0  0  8
 0  0  0  0  0  8  0  8  8  0  8  8  0  8  0  8  0  8  8  8  8  8  8  8  0  8  8  0  0  0  8  8  0  0  0  0  8  8  8  8  8  8  0  8  8  0  0  8  0  8  0

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

Homogenous weight enumerator: w(x)=1x^0+91x^46+228x^47+331x^48+488x^49+547x^50+764x^51+535x^52+464x^53+317x^54+220x^55+88x^56+8x^57+3x^58+4x^59+2x^60+2x^66+3x^68

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 0.285 seconds.