The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+114x^56+12x^60+1x^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 0.155 seconds.