The generator matrix

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

generates a code of length 57 over Z16 who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+130x^49+440x^50+938x^51+1768x^52+2882x^53+5204x^54+7244x^55+9205x^56+10064x^57+9426x^58+7070x^59+5013x^60+2792x^61+1780x^62+916x^63+338x^64+184x^65+69x^66+20x^67+25x^68+10x^69+7x^70+4x^71+2x^73+1x^74+2x^76+1x^78

The gray image is a code over GF(2) with n=456, k=16 and d=196.
This code was found by Heurico 1.16 in 40.9 seconds.