The generator matrix

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

generates a code of length 57 over Z16 who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+600x^51+2188x^52+3978x^53+5330x^54+7228x^55+9064x^56+9014x^57+8850x^58+7678x^59+5485x^60+3304x^61+1598x^62+702x^63+337x^64+106x^65+38x^66+14x^67+5x^68+14x^69+2x^71

The gray image is a code over GF(2) with n=456, k=16 and d=204.
This code was found by Heurico 1.16 in 29.7 seconds.