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  1  1  1  1  1  1  1  2  2  2  2  4  1  1  1  1  1  1  4  1  2  2  1  4  2  8  4  4  4
 0 12  0  0  0  0  0  0  0  0  4 12 12  8  4  4  8  4  0  4  0  4  8  4  8  4 12 12  0  4  8 12  4  8 12 12 12  4 12  4  8  0  4  8 12 12  4  4  4  8  0  4  8  0 12  0
 0  0 12  0  0  0  4 12 12  8  4  4  8  4  4  0  8 12  8  4  0  8  8 12  4  8  8  8  4  8  4 12 12  4  0  8  0  8  0  4  0  0  0  0  0 12  8 12  0  4  0  4  4  4  8  8
 0  0  0 12  0  4  4  4  0  8  0  0  0  0  4 12  4  8  0  8 12  4  8 12  4  4  0 12  4  0  8  4 12  8  4  4 12  4 12  4  0  8  0  4  0  4 12  8  8  8  8  8 12 12  0 12
 0  0  0  0 12  4  8  4  4  0  8  4 12 12  4  8  8  4 12  0  4 12  4 12  0  4  8  8  4 12  8  8  8  8 12  4 12 12  4  4 12  8  4 12 12  0  4  8  4 12  4  0  8  8  8  4
 0  0  0  0  0  8  8  0  8  8  0  0  0  0  0  8  8  8  8  8  0  8  0  8  0  0  8  0  8  8  8  8  0  0  0  0  0  0  8  8  8  8  8  8  0  0  0  0  8  8  0  8  0  8  8  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+16x^49+288x^50+72x^51+461x^52+452x^53+1052x^54+1004x^55+1275x^56+984x^57+1074x^58+448x^59+410x^60+84x^61+222x^62+12x^63+124x^64+46x^66+8x^68+6x^70+7x^72+1x^84

The gray image is a code over GF(2) with n=448, k=13 and d=192.
This code was found by Heurico 1.16 in 1.54 seconds.