The generator matrix

 1  0  1  1  1  6  1 12  1  1  1  6  1  1  0  1  1 10  1  1 14  1  8  1  1  1  4  1 12 14  1  1  1  1  1  1  1  4  1  4  8  1  1  1  2  1 12  1  1 14  1  4 14  1  1  0
 0  1 11  6 13  1  7  1  8  2  1  1 11  8  1  6 13  1  8  5  1  3  1  6 13  4  1  3  1  1  7  6  5 10  6 15  0  1  7  1  1 11 14  0  1  5  1  7  2  1  1  1  1 12  5  1
 0  0 12  0  4  0  4  0  4  0  4  4  0  8  4  0  8  8 12  4  0  4  4 12  8 12  8  8  4 12  8  8 12  4  4  0  4 12  0  0  8  0 12 12  4  8  8 12  0 12  0 12  8  8 12  8
 0  0  0 12  0  0  0  8  8 12  0  4 12 12 12  8 12  0 12  4  4  4  0  4  0  8  4  8 12  8  4  8  4  8  4  8  4  0  4  4  0  4  0 12  8  0  4  0 12  0 12 12  8  8 12  8
 0  0  0  0  8  0  8  8  8  8  0  0  8  0  0  0  0  8  8  0  0  8  8  0  8  8  8  0  8  8  8  8  8  0  8  0  0  0  0  8  0  0  0  0  0  8  0  8  8  0  0  8  0  8  0  8
 0  0  0  0  0  8  8  0  0  0  8  8  8  8  0  8  0  8  8  0  8  8  8  0  0  8  8  8  8  0  0  0  0  0  0  0  8  8  8  0  8  0  8  0  8  8  0  0  8  0  8  8  0  8  8  8

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

Homogenous weight enumerator: w(x)=1x^0+50x^49+161x^50+372x^51+857x^52+1194x^53+2143x^54+1998x^55+2942x^56+1988x^57+2126x^58+1162x^59+821x^60+334x^61+132x^62+32x^63+4x^64+14x^65+8x^66+14x^67+10x^68+4x^69+4x^70+6x^71+5x^72+1x^74+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 3.09 seconds.