The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+336x^52+936x^53+1856x^54+3048x^55+3485x^56+4564x^57+4764x^58+4424x^59+3375x^60+2992x^61+1518x^62+792x^63+418x^64+116x^65+68x^66+24x^67+25x^68+14x^70+8x^72+4x^74

The gray image is a code over GF(2) with n=464, k=15 and d=208.
This code was found by Heurico 1.16 in 10.5 seconds.