The generator matrix

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

generates a code of length 53 over Z16 who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+286x^50+360x^51+340x^52+232x^53+282x^54+248x^55+166x^56+56x^57+62x^58+3x^60+6x^62+1x^64+4x^66+1x^76

The gray image is a code over GF(2) with n=424, k=11 and d=200.
This code was found by Heurico 1.16 in 9.98 seconds.