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

generates a code of length 56 over Z16 who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+38x^49+92x^50+120x^51+158x^52+266x^53+435x^54+622x^55+754x^56+638x^57+378x^58+228x^59+132x^60+60x^61+36x^62+38x^63+33x^64+16x^65+14x^66+16x^67+10x^68+6x^69+4x^70+1x^86

The gray image is a code over GF(2) with n=448, k=12 and d=196.
This code was found by Heurico 1.16 in 0.561 seconds.