The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+340x^52+288x^53+945x^54+712x^55+1348x^56+1056x^57+1240x^58+752x^59+932x^60+256x^61+238x^62+8x^63+36x^64+8x^66+24x^68+1x^70+6x^72+1x^80

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 45 seconds.