The generator matrix

 1  0  1  1  6  1  4  1  1  1  1  2  1  1  8  1 10  1  8  1  1  1  1  1  6 10  1  0  1 12  1  2  1  1  1  6  4  1  1  1  2  1  1  1  8  1  6 12  2  6  6 14  4  1  1  2
 0  1  1  6  1  7  1  4  3  5  2  1  3  8  1 13  1 10  1 11 12  9  6  0  1  1 13  1  5  1  6  1  4 15 11  1  1  3  2  0  8  5  7 10  1 14  1  1  6  1  1  1 12 10  1  4
 0  0  2  0  0  2 10 10  0  8 10 10 14  4 10 10  8  4  4 12  0  8 14  6 14  6  4 14  6  4  6 12 10  8 10  2 14  6  4  8  2  0  4 10 10 12 14  6  2 12  0 14  2 10  2 10
 0  0  0  8  0  0  8  0  8  8  0  8  0  8  8  0  0  8  0  8  0  8  8  8  0  0  0  8  8  8  8  8  8  0  8  8  0  0  0  0  8  0  0  0  0  0  8  0  8  0  0  0  0  8  0  8
 0  0  0  0  8  0  0  0  0  8  8  8  8  8  0  8  0  0  8  0  8  8  8  8  8  8  0  8  0  0  0  8  0  8  0  0  0  0  8  0  0  8  0  0  8  0  8  8  0  8  8  0  8  0  0  0
 0  0  0  0  0  8  8  0  8  8  0  8  0  8  0  8  8  0  8  0  8  0  0  8  0  8  8  0  0  8  8  0  0  8  8  8  0  0  0  8  8  8  0  0  0  8  0  0  0  0  8  8  0  0  8  8

generates a code of length 56 over Z16 who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+198x^50+384x^51+1086x^52+980x^53+2525x^54+1744x^55+2940x^56+1716x^57+2240x^58+944x^59+870x^60+300x^61+250x^62+64x^63+89x^64+12x^65+30x^66+4x^68+1x^70+2x^72+4x^74

The gray image is a code over GF(2) with n=448, k=14 and d=200.
This code was found by Heurico 1.16 in 2.97 seconds.