The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+141x^50+184x^51+451x^52+608x^53+946x^54+1240x^55+1081x^56+1280x^57+936x^58+616x^59+351x^60+160x^61+143x^62+8x^63+30x^64+4x^66+2x^68+3x^70+4x^72+3x^74

The gray image is a code over GF(2) with n=448, k=13 and d=200.
This code was found by Heurico 1.16 in 91.6 seconds.