The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+374x^51+895x^52+1842x^53+1813x^54+2502x^55+2095x^56+2540x^57+1386x^58+1382x^59+749x^60+458x^61+183x^62+84x^63+36x^64+24x^65+9x^66+8x^67+2x^71+1x^74

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 5.29 seconds.