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

generates a code of length 58 over Z16 who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+211x^52+244x^53+506x^54+536x^55+1135x^56+860x^57+1526x^58+724x^59+1079x^60+424x^61+418x^62+168x^63+144x^64+100x^65+66x^66+12x^67+17x^68+4x^69+12x^70+4x^72+1x^84

The gray image is a code over GF(2) with n=464, k=13 and d=208.
This code was found by Heurico 1.16 in 1.28 seconds.