The generator matrix

 1  0  1  1  1  4  1  1  6  1  1  4 10  1  1  1  1  6  1  4  1  1  1  4  1  1  1 12  1  1  8 14  2 10  1  1 14  1  1 10  1  1  4  4  1  1  8 10  2  1 12  1  1 10  8  1
 0  1  1  0  3  1  5  4  1  8  3  1  1 10 15  2 13  1 11  1  2 14 14  1  7  5 14  1  6  4  1  1  1  1  9  9  1  8  1  1 10  0  1  1 14 11  1  1  6 11  4  4 15  1  1  8
 0  0  2  0  0  0  2 10  6  2  8 14  0  8  2 10  4 12 14 14  6  4  6 10  0 14 10 14  4 12  8  0 10  6 10  2 12 14  4  0  6  8 12  0 14  8  6 14  6  4  2 12 12  6  4  4
 0  0  0  2  0  2  2  8 14 14  6  4  6 14 10  6  2 12  8 10  4  0  2  0  4  6  8  8 10  0  6  8  0  6 10 12  2  0 14 12  6  4 12 14 10  8  0  4 10  0  4  6 12  0 14  0
 0  0  0  0  8  0  0  8  8  8  8  8  0  0  0  8  8  0  0  8  8  0  8  8  0  8  0  0  8  8  8  8  8  0  8  0  8  0  0  8  0  0  8  0  0  8  0  8  8  0  0  8  0  8  8  0
 0  0  0  0  0  8  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  8  0  8  8  8  8  0  0  8  0  8  0  8  0  8  0  0  0  0  0  8  8  8  8  8  8  0  0  0  0  8  0  0  0  0

generates a code of length 56 over Z16 who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+119x^48+428x^49+855x^50+1884x^51+2701x^52+4908x^53+6943x^54+9862x^55+10014x^56+10264x^57+6943x^58+4778x^59+2777x^60+1622x^61+678x^62+404x^63+151x^64+120x^65+34x^66+30x^67+10x^68+2x^69+2x^70+2x^71+3x^72+1x^78

The gray image is a code over GF(2) with n=448, k=16 and d=192.
This code was found by Heurico 1.16 in 39.9 seconds.