The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+76x^49+189x^50+378x^51+809x^52+1450x^53+2419x^54+3700x^55+4805x^56+5250x^57+4812x^58+3708x^59+2410x^60+1388x^61+712x^62+286x^63+142x^64+70x^65+49x^66+54x^67+20x^68+22x^69+9x^70+2x^71+4x^72+2x^74+1x^76

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 13.5 seconds.