The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+22x^50+344x^51+40x^52+208x^53+40x^54+344x^55+22x^56+1x^64+2x^74

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 0.0684 seconds.