The generator matrix

 1  0  1  1  1  6  1  1 12  1  1 10  0  1  1  6  1  1 12  1  1 10  1  1  0  1  1  1  6  1  1 10 12  1  1  1  0  6  1  1 10  1  1  1  1  1  1  1  1  1  1  6  1  1  1  1
 0  1  3  6  5  1 12  7  1 10  9  1  1  0  5  1  6  3  1 15 12  1  9 10  1  0  3  5  1  6 15  1  1  3  9 15  1  1 12 10  1  6  5 12  0  3  3 10 10  6  5  1 15  6  3  0
 0  0  8  0  0  0  0  0  0  0  0  0  0  0  8  0  0  0  8  8  8  8  8  8  8  0  8  8  0  8  0  0  0  0  8  8  8  0  8  0  8  8  8  8  0  8  0  0  0  0  8  0  8  0  8  0
 0  0  0  8  0  0  0  0  0  0  0  0  0  8  0  8  0  8  0  0  8  0  8  8  8  8  8  0  0  8  8  0  8  8  0  0  0  8  8  8  0  8  0  0  8  0  8  8  0  8  8  8  0  8  8  0
 0  0  0  0  8  0  0  0  0  0  0  8  8  0  8  8  8  8  8  0  0  8  0  8  8  8  8  0  8  8  0  0  8  0  0  0  0  0  0  0  8  0  8  0  8  8  8  8  0  0  0  0  8  0  8  0
 0  0  0  0  0  8  0  0  0  0  8  8  8  0  8  0  0  8  8  8  8  0  0  8  8  8  0  8  0  0  8  0  8  8  0  8  8  0  0  0  0  0  0  0  8  8  0  0  8  0  0  8  0  8  8  8
 0  0  0  0  0  0  8  0  0  8  8  0  0  8  8  0  0  8  8  0  0  8  8  8  8  0  0  0  8  8  0  8  8  8  8  8  0  0  0  0  0  8  0  0  0  8  0  0  8  8  8  8  8  0  0  0
 0  0  0  0  0  0  0  8  0  8  0  0  0  0  0  0  8  8  0  8  0  8  8  0  8  8  8  0  8  8  0  8  0  8  8  0  8  0  8  8  0  0  0  8  8  8  0  8  8  0  8  0  8  8  0  0
 0  0  0  0  0  0  0  0  8  0  8  8  0  0  8  8  8  8  0  8  0  0  8  8  0  0  8  0  8  0  8  8  0  0  0  8  0  8  0  0  0  8  8  0  8  8  0  0  0  8  0  8  8  8  8  0

generates a code of length 56 over Z16 who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+27x^46+157x^48+96x^49+352x^50+736x^51+1035x^52+3104x^53+2705x^54+6304x^55+3779x^56+6304x^57+2700x^58+3104x^59+1026x^60+736x^61+327x^62+96x^63+119x^64+16x^66+15x^68+11x^70+7x^72+4x^74+4x^76+2x^78+1x^80

The gray image is a code over GF(2) with n=448, k=15 and d=184.
This code was found by Heurico 1.16 in 11.2 seconds.