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

generates a code of length 56 over Z16 who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+157x^48+40x^50+101x^52+376x^54+2799x^56+344x^58+119x^60+8x^62+101x^64+35x^68+12x^72+1x^76+1x^80+1x^88

The gray image is a code over GF(2) with n=448, k=12 and d=192.
This code was found by Heurico 1.16 in 61.2 seconds.