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

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

Homogenous weight enumerator: w(x)=1x^0+158x^50+268x^51+451x^52+680x^53+972x^54+960x^55+1342x^56+1124x^57+840x^58+540x^59+362x^60+160x^61+144x^62+88x^63+59x^64+20x^65+10x^66+6x^68+4x^70+2x^72+1x^84

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 1.25 seconds.