The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  1  1  1  2  1  1  2  1  4  1  1  0  1  1  1  1  1  1  4  2  1  1  0  1  1  2  4  1  4  1  1  2  2  1
 0 12  0 12  0 12  0 12  0  4  8  0 12 12  4  0  8  0  8  0 12 12  0 12  4 12 12  4 12 12 12 12  0  4  0  4  8  0  8  4 12 12 12  4  4  8  4 12 12 12 12  0 12 12 12  0
 0  0  8  0  0  0  0  0  0  0  8  8  0  8  8  0  8  0  8  8  0  0  8  0  8  0  8  0  0  0  0  8  0  0  8  8  8  8  8  8  0  8  8  8  8  8  0  8  0  0  8  8  0  8  8  0
 0  0  0  8  0  0  0  0  0  8  0  0  0  8  8  0  0  8  8  8  0  8  8  8  0  8  0  0  8  8  0  8  8  8  0  0  0  8  8  0  8  0  8  0  8  0  8  0  0  8  8  0  8  8  0  0
 0  0  0  0  8  0  0  0  0  0  0  8  0  0  0  8  0  8  8  8  0  8  0  8  8  0  0  0  0  8  8  0  8  8  8  0  8  8  0  8  0  8  8  8  0  0  8  0  8  8  0  0  0  0  0  0
 0  0  0  0  0  8  0  0  0  0  0  0  8  8  8  0  0  0  0  0  0  8  0  0  8  0  0  8  8  8  0  0  8  8  8  8  8  8  8  8  8  0  8  0  8  8  0  0  0  0  0  8  8  0  0  0
 0  0  0  0  0  0  8  0  0  0  0  8  0  0  0  8  8  8  8  0  8  0  8  8  8  8  8  8  8  0  0  8  8  0  0  8  8  0  0  0  0  0  0  8  8  0  8  8  8  0  0  0  8  8  0  0
 0  0  0  0  0  0  0  8  0  8  0  0  8  8  0  8  8  8  0  0  8  8  0  8  0  0  0  8  0  0  0  8  8  8  0  0  8  0  8  8  8  0  0  8  8  0  0  8  0  8  0  8  8  8  8  8
 0  0  0  0  0  0  0  0  8  0  8  8  8  0  8  8  8  0  0  0  8  0  0  8  8  8  8  0  0  0  8  0  0  8  0  8  0  8  0  8  0  8  0  8  0  8  0  0  8  8  0  8  8  8  0  0

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

Homogenous weight enumerator: w(x)=1x^0+30x^46+26x^47+69x^48+78x^49+152x^50+132x^51+463x^52+156x^53+1624x^54+120x^55+2543x^56+120x^57+1616x^58+156x^59+437x^60+132x^61+122x^62+78x^63+51x^64+26x^65+20x^66+10x^68+16x^70+7x^72+4x^74+1x^76+1x^80+1x^84

The gray image is a code over GF(2) with n=448, k=13 and d=184.
This code was found by Heurico 1.16 in 1.73 seconds.