The generator matrix

 1  0  0  1  1  1 10  2  1  1  1  1 14 12  1  1 12  0  1  1  8  1  1  6  6 10  1  1  6  1  1  1  1  0  1  8  1  4  1  1  6  6  8 12  4  1 10  1  1  1  1  2  0 10  1  1
 0  1  0  0  5 13  1  6  1  9  4  4  1  1 14  3  1 10 10 15  1 15 14  1  4  1 11 10  1  5 11 12 12  1  2 10 12  1  5 15  1  1  1  1 14  6 14  9  2 10  2  1  1  1 12  6
 0  0  1 11  7  4  7  1  1  2  6 13  6  5  5  1 15  1  6 12 14 14  4 12  1  1  3 15 11  8  5 14  5 12  4  1  7 14  1  7 13  1  0 15  1 15  1 10 10 15  1 10  7  7  9 12
 0  0  0 12 12  0 12  4  0 12  4  8  4  0 12 12  4  8  0  4  0  8  4  0 12 12  8  8  8  8  0  0  4  4  8  4  8 12 12  0  4  8 12  8  0  0  0  8 12  4  4  8 12  0  0 12

generates a code of length 56 over Z16 who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+304x^51+1094x^52+1584x^53+1978x^54+2454x^55+2304x^56+2146x^57+1728x^58+1128x^59+853x^60+468x^61+194x^62+70x^63+30x^64+26x^65+4x^66+12x^67+5x^68+1x^72

The gray image is a code over GF(2) with n=448, k=14 and d=204.
This code was found by Heurico 1.16 in 2.41 seconds.