The generator matrix

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

generates a code of length 57 over Z16 who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+149x^52+524x^53+862x^54+1016x^55+1118x^56+1124x^57+1032x^58+912x^59+719x^60+452x^61+134x^62+40x^63+56x^64+12x^65+20x^66+16x^67+2x^68+1x^72+2x^76

The gray image is a code over GF(2) with n=456, k=13 and d=208.
This code was found by Heurico 1.16 in 0.793 seconds.