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

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

Homogenous weight enumerator: w(x)=1x^0+126x^47+352x^48+928x^49+1309x^50+2068x^51+2769x^52+5290x^53+5925x^54+10088x^55+7989x^56+9730x^57+5841x^58+5668x^59+3016x^60+2100x^61+1061x^62+634x^63+318x^64+172x^65+68x^66+40x^67+18x^68+18x^69+2x^70+2x^73+1x^74+1x^76+1x^90

The gray image is a code over GF(2) with n=448, k=16 and d=188.
This code was found by Heurico 1.16 in 57.3 seconds.