The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+40x^56+4x^57+11x^58+4x^59+3x^60+1x^62

The gray image is a code over GF(2) with n=448, k=6 and d=224.
This code was found by Heurico 1.16 in 0.0824 seconds.