The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  0  1  1  8  2  1  1  1  1  4  2  0  1  1  2  4  1  1  8  1  2  1 12  1  2  1  1  2  2  1  1  4 12  1  1  1  4
 0  2  0  6  4  6 12  2  6 14  8 12  0  2 10 12  0  6  6  2  4  2  2 14  2 12  6  4  2  6  2  0 14 14  2  4 14  2 12  2 10  2  4 14  8  2  8  2 10 10  2  2 14  6  8  4
 0  0 12  0  4  0  0  8  4 12  0  4  4  4  4  0  8  0 12  4  0  8  8  8  4 12  4 12  8  8  8  8  8 12  4  8 12 12 12  8  4  0  8 12 12  4 12  8 12  4 12  4  4  4  0  8
 0  0  0 12  0  0  0 12  4  8 12 12  4  0 12 12  8  0 12 12  4 12 12  4  0  4  4  8  4  0  0  4 12  8  8  8  0  8 12 12  4  8  8  0  8 12 12  4 12 12  0  4  0  0 12 12
 0  0  0  0  8  0  0  0  0  0  0  0  8  0  0  8  8  8  0  8  8  8  0  8  0  8  0  8  0  0  8  0  8  8  0  8  8  8  8  0  8  8  0  0  8  8  0  0  0  8  8  0  0  8  8  0
 0  0  0  0  0  8  0  8  0  8  8  8  8  0  8  8  0  0  8  8  8  8  8  0  8  0  0  8  0  0  8  0  0  0  0  8  0  0  0  0  8  8  8  8  0  0  0  8  0  8  8  8  0  0  0  8
 0  0  0  0  0  0  8  0  0  0  0  8  8  0  0  0  8  8  0  8  8  8  8  0  8  0  8  8  0  8  8  0  0  8  8  8  0  0  0  8  0  0  8  0  0  8  8  0  0  8  0  8  8  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+137x^48+56x^49+456x^50+364x^51+918x^52+1176x^53+1962x^54+2004x^55+2453x^56+1968x^57+1776x^58+1172x^59+977x^60+376x^61+300x^62+44x^63+146x^64+8x^65+40x^66+32x^68+10x^70+7x^72+1x^76

The gray image is a code over GF(2) with n=448, k=14 and d=192.
This code was found by Heurico 1.16 in 5.1 seconds.