The generator matrix

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

generates a code of length 52 over Z16 who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+120x^52+5x^56+1x^64+1x^72

The gray image is a code over GF(2) with n=416, k=7 and d=208.
This code was found by Heurico 1.16 in 0.0738 seconds.