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

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

Homogenous weight enumerator: w(x)=1x^0+140x^49+325x^50+710x^51+720x^52+1518x^53+1365x^54+2448x^55+1925x^56+2722x^57+1400x^58+1448x^59+553x^60+488x^61+239x^62+164x^63+84x^64+70x^65+25x^66+10x^67+12x^68+6x^69+6x^70+4x^71+1x^76

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 25.9 seconds.