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

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

Homogenous weight enumerator: w(x)=1x^0+112x^48+366x^49+650x^50+1156x^51+1645x^52+2418x^53+3223x^54+4584x^55+4657x^56+4536x^57+3317x^58+2380x^59+1465x^60+974x^61+588x^62+378x^63+168x^64+86x^65+29x^66+12x^67+14x^68+4x^69+2x^71+2x^72+1x^78

The gray image is a code over GF(2) with n=448, k=15 and d=192.
This code was found by Heurico 1.16 in 15.1 seconds.