The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+39x^48+210x^49+466x^50+1098x^51+1568x^52+2394x^53+4197x^54+3972x^55+5130x^56+4112x^57+3809x^58+2360x^59+1713x^60+908x^61+331x^62+224x^63+111x^64+54x^65+25x^66+22x^67+11x^68+2x^69+4x^70+4x^71+3x^72

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 10.8 seconds.