The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+422x^52+898x^53+1737x^54+2064x^55+2307x^56+2134x^57+2126x^58+1810x^59+1371x^60+718x^61+490x^62+136x^63+72x^64+38x^65+30x^66+6x^67+19x^68+4x^69+1x^70

The gray image is a code over GF(2) with n=456, k=14 and d=208.
This code was found by Heurico 1.16 in 2.2 seconds.