The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+52x^49+329x^50+812x^51+1601x^52+3542x^53+4796x^54+7918x^55+8147x^56+10610x^57+8999x^58+8228x^59+4416x^60+3314x^61+1544x^62+680x^63+275x^64+138x^65+63x^66+20x^67+23x^68+8x^69+12x^70+2x^71+1x^72+1x^74+4x^75

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 32.7 seconds.