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  2  0  2  0  1  2  0  1  8  1  1  1  1  2 12  1  2  1  1  1 12  0  2  2  1  1  1  4  1  4  8  1
 0  2  0  0  0  2  6 14  8  8 14  6 12 10  8  6 12 14  6 14  0  0 10  4 10  2 14 12 14  2  4  4  2  0  4  0 10  2  2  0  2 10 14  6  2  8  6 10 10  6  8  2  4  2  4  0
 0  0  2  0  2  2 10  0 12 14  8  2 12 12  2 14  2 10 14  0  4  6  4  8  6  4 14  2 14  0 12  4 14  2 14 12 10 10  8  8  0 10  2  4  8  8 14  0 14 12  2 10  2  6  2  0
 0  0  0  2  2  8 10  2  4  0 14 12  2  0  6  6  8  8  2  4 14  2 10 12  8  4 10  4  8 10  2  8  6 12  0 10 10 12 10  6  8 12  2 10  6  2 12  0  4  4  8 10  4 12  8  0
 0  0  0  0  8  8  0  8  8  8  0  0  8  8  0  8  8  0  8  8  0  0  8  0  0  0  8  8  0  8  8  8  0  8  0  0  0  8  8  8  8  8  8  8  0  0  0  0  0  0  8  8  0  8  0  8

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

Homogenous weight enumerator: w(x)=1x^0+100x^49+352x^50+592x^51+951x^52+1234x^53+1842x^54+2006x^55+2468x^56+1970x^57+1980x^58+1048x^59+702x^60+496x^61+245x^62+182x^63+123x^64+38x^65+28x^66+12x^67+11x^68+2x^69+1x^78

The gray image is a code over GF(2) with n=448, k=14 and d=196.
This code was found by Heurico 1.16 in 4.12 seconds.