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

generates a code of length 63 over Z16 who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+174x^56+356x^57+800x^58+716x^59+1476x^60+1412x^61+2496x^62+1808x^63+2442x^64+1416x^65+1454x^66+528x^67+527x^68+276x^69+260x^70+112x^71+79x^72+28x^73+14x^74+4x^75+4x^76+1x^92

The gray image is a code over GF(2) with n=504, k=14 and d=224.
This code was found by Heurico 1.16 in 4.77 seconds.