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

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

Homogenous weight enumerator: w(x)=1x^0+60x^49+102x^50+106x^51+68x^52+172x^53+416x^54+706x^55+894x^56+688x^57+418x^58+162x^59+50x^60+76x^61+70x^62+46x^63+8x^64+28x^65+16x^66+4x^67+2x^68+2x^70+1x^96

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 20.5 seconds.