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

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

Homogenous weight enumerator: w(x)=1x^0+25x^50+80x^51+38x^52+736x^53+38x^54+80x^55+25x^56+1x^106

The gray image is a code over GF(2) with n=424, k=10 and d=200.
This code was found by Heurico 1.16 in 0.152 seconds.