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

generates a code of length 56 over Z16 who´s minimum homogenous weight is 47.

Homogenous weight enumerator: w(x)=1x^0+70x^47+187x^48+322x^49+669x^50+880x^51+1417x^52+2554x^53+2953x^54+5408x^55+3870x^56+5442x^57+3018x^58+2510x^59+1491x^60+810x^61+482x^62+332x^63+175x^64+84x^65+41x^66+10x^67+19x^68+4x^69+5x^70+6x^71+6x^72+1x^76+1x^80

The gray image is a code over GF(2) with n=448, k=15 and d=188.
This code was found by Heurico 1.16 in 78.9 seconds.