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  2
 0  2 12  6  0  6 12 10  0  6 10 12  0  6 12 10 10  0 12  6  8 14  4 10  0  6 12 10  8 14  4  2  0  6 12  2  8 14  4 10  8 14  4  2  8  8 14  2  0  8 14 14 12
 0  0  8  0  0  0  8  0  0  8  8  8  0  8  8  8  0  8  0  8  8  0  0  8  8  0  0  8  8  8  0  0  8  0  0  8  8  8  8  0  0  8  8  8  0  0  0  0  8  8  0  8  8
 0  0  0  8  0  0  0  8  8  8  8  8  8  0  8  0  0  8  0  8  0  8  8  0  8  0  0  8  0  0  8  8  0  8  8  0  8  8  0  8  0  8  8  0  8  0  8  8  0  8  0  0  0
 0  0  0  0  8  8  8  8  8  0  8  0  0  8  8  0  8  0  0  8  0  8  0  8  8  0  8  0  8  0  8  0  8  8  8  8  8  0  0  0  8  8  0  0  0  0  0  8  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+61x^50+138x^52+640x^53+122x^54+52x^56+9x^58+1x^104

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 0.11 seconds.