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  1  1  1  1  1  1  1  1  1  2  1  1  1  4  1  1  1  4  1  1  2  1  1  2  4  1  1
 0 12  0  4  0  0  4  4  8  8  4 12 12 12  0  8  0  4  8  4 12  0  0  4  4  4  0  8  8  0  4 12  0  8  8  0 12  8 12 12  8  8  0 12  4  0 12  4 12  8  0  8 12 12  8  0
 0  0 12  4  0 12 12  0  8  4  4  0  8  4  8 12  0 12 12  8  0  4  0  4  8  8  0  0  4  4  4  4  0  4  8 12  8  4  0  8  4  0 12  8  0 12  8  0  0  4 12 12  8  0 12  0
 0  0  0  8  0  0  8  0  0  0  0  8  8  0  8  8  8  8  8  8  0  8  8  0  0  8  0  8  8  0  8  0  0  0  0  0  8  8  8  0  8  0  0  0  0  8  8  0  8  0  8  0  0  8  0  0
 0  0  0  0  8  0  0  0  0  8  8  0  8  0  8  8  0  8  0  0  8  8  8  8  8  8  8  0  0  8  8  0  0  0  8  8  0  8  8  8  8  8  0  8  0  0  0  8  8  8  0  8  8  8  8  0
 0  0  0  0  0  8  8  8  8  8  8  8  8  8  0  0  0  8  8  0  8  8  8  0  0  0  8  8  0  0  0  0  8  0  0  8  8  0  0  8  8  0  0  0  0  8  0  8  8  8  0  8  8  8  0  0

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

Homogenous weight enumerator: w(x)=1x^0+66x^50+94x^52+96x^53+156x^54+416x^55+432x^56+416x^57+122x^58+96x^59+65x^60+64x^62+14x^64+8x^66+1x^72+1x^100

The gray image is a code over GF(2) with n=448, k=11 and d=200.
This code was found by Heurico 1.16 in 59.8 seconds.