The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 12  0  0  1  2  2  1 12  8  1  2  1  2  8  2  1  2 12  2 12  1  2  1 12  0  1  1  1 12  2  2  1
 0  2  0  0  0  2 14  2  4 12 14 10 12 14 12 14  4 14  0  4  2 10  4  6  6  2 12  2 12 14 10  4  2  2 14 14  6  8  4  8 10  0  2 10  2  6  8  0  2 12  4 12  2  0 14 10  8
 0  0  2  0  2  2 10  8  0  0  2 10  6  4 14  4  8  8  4  2 14 10  2  0  4  6  2  4  0  2 12 14  0  4  2 10  0  2  8 14 14 12  2  6 14 14 10 10 10 12  8  8  2  2 14  0  0
 0  0  0  2  2  8  2  6 14  4  4 14 14 10 12  4 10 14 12  6 12  6 12  0 12  0 12  2  8  6  0  2 10  8  6  8  6 10  2 12 12  2  6 14  2 14 10  8  2  2 10  8 10  4  0 14 12
 0  0  0  0  4  0  4 12 12 12 12  8  8  0 12 12 12  0  0  4  0 12 12 12  8  8  0  8  0  8  4  0 12  8  0  4  4 12  8  8  8 12 12  0  4  8  4 12  0  0  4  4  4 12  0  0  0

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

Homogenous weight enumerator: w(x)=1x^0+102x^49+367x^50+762x^51+1258x^52+1804x^53+2548x^54+3398x^55+4046x^56+4316x^57+4096x^58+3460x^59+2583x^60+1720x^61+978x^62+568x^63+378x^64+206x^65+105x^66+26x^67+19x^68+12x^69+2x^70+10x^71+3x^72

The gray image is a code over GF(2) with n=456, k=15 and d=196.
This code was found by Heurico 1.16 in 15.8 seconds.