The generator matrix

 1  0  1  1  1  6  1  1  8  1  1 14  4  1  1 10  1  1 12  1  1  2  1  1  1  1  1 14  0  1  1  2  1  1  6  1  1  1  2  0  1  1  8  6 12  8  1 10  1  1  1  1  6  1  2  1
 0  1 11  6 13  1 12  7  1 10  1  1  1  8  3  1 14  5  1  4  9  1  2 15  0  7  5  1  1  3  8  1 11 13  1 11  1  6  1  1 10  0  1  1  1  1  4  1 14  4  0  9  1 14  6  0
 0  0 12  0  4  0  0  4  4  8  4 12 12  4  8  0  4  0  0  4  8  4 12  8  8 12  8 12  8  8  4 12 12  4  8 12 12  8 12  8  8  4 12  8  0  4 12 12  4  4  0  8  4 12  0  0
 0  0  0  8  0  0  0  0  0  0  8  8  0  8  8  0  8  8  8  0  0  8  8  8  0  8  8  0  0  0  8  8  0  8  0  0  0  8  0  0  8  8  0  0  8  8  8  8  0  0  0  8  0  0  0  0
 0  0  0  0  8  0  0  8  8  0  8  0  0  8  0  8  0  0  8  8  8  0  0  0  0  8  8  0  0  8  8  8  0  0  8  0  8  8  8  0  8  8  0  0  8  0  0  8  8  0  8  0  0  0  0  0
 0  0  0  0  0  8  0  8  8  8  0  8  8  8  0  8  8  0  0  0  8  8  0  8  8  8  0  0  8  8  8  8  8  0  0  0  8  8  0  0  0  0  0  0  0  0  0  0  8  0  0  0  8  8  0  0
 0  0  0  0  0  0  8  0  0  8  0  0  8  0  0  8  0  8  8  8  0  8  0  0  0  8  0  8  8  8  8  8  8  8  8  8  8  0  8  8  8  8  0  0  0  0  8  0  8  8  8  0  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+28x^48+84x^49+149x^50+432x^51+755x^52+1324x^53+1890x^54+2292x^55+2581x^56+2248x^57+1908x^58+1298x^59+700x^60+420x^61+123x^62+68x^63+19x^64+12x^65+15x^66+4x^67+9x^68+8x^69+10x^70+3x^72+2x^75+1x^78

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 2.99 seconds.