The generator matrix

 1  0  1  1  1  6  1  1  0  6  1  1  8  1  1  2  1  1  1  4  1  1  1 14  1  1  6  0  1  1  1  1  4  1  1  1 10  1 10  1  8  8  1  1  1  4  1 12  1  1  8  1  1  1  6  0
 0  1 11  6  1  1  8 11  1  1  6 13  1  8  5  1 10  3 14  1 11 13  0  1 12  5  1  1  6 15  1  4  1  3  9 15  1  1  1 14  1  1 10  7  7  1  6  1 12 10  1  0 13  6  1  1
 0  0 12  0  0  0  0  0  0  8  8 12  0  8  8  0  8  8  8  0  0  4  4  4  4  4 12 12  0  8  4 12  0 12  0 12  8  4  4  0 12  4  4  4 12  8  4  0  4  4  8  8 12  4  4  8
 0  0  0 12  0  0 12  8  4 12  8  0  8  8  0  4  4  4  0 12  4 12  0  8 12  4  0 12  4  0  4  4  0 12  0  8  0  8  0  8 12  4  8 12 12 12  8  8  8  4 12  4  0  4  4 12
 0  0  0  0  4  0  8  4  4 12  0  0  4  4  0  0  4 12 12  0  0  4 12  8  8  8  4  0 12  8 12 12  4  0  8  4  8  4 12  4 12 12 12 12  8  4 12  8  8  4 12 12  8  0  8  4
 0  0  0  0  0  8  8  8  8  0  8  8  0  8  8  0  8  0  0  8  0  0  0  0  0  8  0  8  0  0  8  0  8  0  0  0  8  8  8  0  8  0  0  0  8  0  8  0  8  8  0  8  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+145x^48+36x^49+486x^50+636x^51+1323x^52+2612x^53+3612x^54+5420x^55+4377x^56+5420x^57+3556x^58+2612x^59+1234x^60+636x^61+392x^62+36x^63+116x^64+70x^66+33x^68+12x^70+1x^72+2x^76

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 11.9 seconds.