The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+120x^56+7x^64

The gray image is a code over GF(2) with n=448, k=7 and d=224.
This code was found by Heurico 1.16 in 0.0975 seconds.