The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+700x^50+1866x^51+3825x^52+5798x^53+7176x^54+8748x^55+9095x^56+9478x^57+7476x^58+5200x^59+3383x^60+1634x^61+736x^62+244x^63+96x^64+50x^65+24x^66+6x^67

The gray image is a code over GF(2) with n=448, k=16 and d=200.
This code was found by Heurico 1.16 in 33 seconds.