The generator matrix

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

generates a code of length 62 over Z16 who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+280x^56+416x^57+1152x^58+1184x^59+2224x^60+1820x^61+2542x^62+1768x^63+2245x^64+1004x^65+908x^66+336x^67+241x^68+84x^69+92x^70+40x^71+29x^72+4x^73+4x^74+3x^76+6x^78+1x^80

The gray image is a code over GF(2) with n=496, k=14 and d=224.
This code was found by Heurico 1.16 in 11.9 seconds.