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

generates a code of length 56 over Z16 who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+42x^46+96x^47+239x^48+352x^49+587x^50+1038x^51+1668x^52+2356x^53+3271x^54+4228x^55+4721x^56+4586x^57+3511x^58+2376x^59+1503x^60+906x^61+522x^62+284x^63+195x^64+110x^65+58x^66+42x^67+57x^68+10x^69+8x^70+1x^78

The gray image is a code over GF(2) with n=448, k=15 and d=184.
This code was found by Heurico 1.16 in 18.2 seconds.