The generator matrix

 1  0  1  1  1 14  1  1  0 14  1  1  1  0  1  2  1  1  1  8  1  1  1  8  1  6  1 10  1  1  1  1 12  1  1  0 14  1  1  1  1 12  2  1  1 12  1  1  6  1  2  1  1  1 12  1
 0  1 11  6  1  1  8  3  1  1 14  9  6  1  3  1 13  0  3  1  8 10  9  1 15  1 14  1 12 13 11  6  1 10 11  1  1 11  9  2  8  1  1  4  7  2  7 14  1 13 10  8 11  6  1  8
 0  0 12  0  0  0  0  8 12  4  4  4 12 12  0  4  8  8 12  8  4  4  4  0  0  4  0  8  4 12  0  8  0 12 12 12  8  4  8 12  0  4  8  0  4  0  8  4  4 12 12 12  4  0  4  0
 0  0  0 12  0  0  8  8  8  8  0  8  8 12 12 12 12 12 12 12 12 12  4  4  4  8  0  0 12  0  4  4 12  0 12  4 12  4  0 12  8  8  4 12  0  8  0 12  0  8  0  8  4  4  4  4
 0  0  0  0  4 12 12  8  4  0  0  4  4  8 12  4  0  4 12  4 12  8  0  0  4 12 12  0  8  8  0 12  4 12  8  8 12 12  8  4  8  0  0  8 12  4  4 12  4  8  8  0  0  4  0  0

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

Homogenous weight enumerator: w(x)=1x^0+60x^49+199x^50+370x^51+808x^52+1320x^53+1884x^54+2374x^55+2515x^56+2424x^57+1786x^58+1228x^59+786x^60+288x^61+139x^62+80x^63+43x^64+28x^65+18x^66+10x^67+6x^68+8x^69+5x^70+2x^71+1x^72+1x^74

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 3.16 seconds.