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  2  1  1  2  4
 0 12  0  4  0  0  4 12  0  0  4 12  0  0  4 12  0  4  8  4 12  8  0 12 12  8  4  8  4  8  4  8  0  4 12  0  8  8 12 12  4  8  8 12  4  4  0  0  8  0  8  4 12
 0  0 12  4  0 12  4  0  0 12  4  0  0 12  4  0  8 12  4  0 12  8  4  8  4  0  8 12 12  8  0  4  8  0  4  4  8 12  8 12 12  0 12  8  0  8  8  8  4  4  4  4  0
 0  0  0  8  0  0  8  0  8  8  0  8  8  8  0  8  8  8  0  0  0  0  8  8  8  8  0  0  0  0  8  8  0  8  0  8  8  0  8  8  0  8  8  0  0  0  8  0  8  0  8  0  8
 0  0  0  0  8  8  8  8  8  8  0  8  0  0  8  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  0  0  8  8  8  0  8  8  0  0  0  8  8  0  8  8  8  8  0  8  8

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

Homogenous weight enumerator: w(x)=1x^0+78x^50+318x^52+256x^53+308x^54+31x^56+30x^58+1x^60+1x^100

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 0.15 seconds.