The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+396x^56+892x^57+2382x^58+2684x^59+3852x^60+3936x^61+4966x^62+3888x^63+3762x^64+2484x^65+1860x^66+844x^67+537x^68+104x^69+94x^70+8x^71+57x^72+8x^73+10x^74+3x^76

The gray image is a code over GF(2) with n=496, k=15 and d=224.
This code was found by Heurico 1.16 in 20 seconds.