The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+350x^52+956x^53+2008x^54+2428x^55+4055x^56+4164x^57+5360x^58+3992x^59+3842x^60+2360x^61+1828x^62+780x^63+336x^64+132x^65+90x^66+32x^67+23x^68+4x^69+24x^70+2x^74+1x^76

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 13.3 seconds.