The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+182x^56+484x^57+1011x^58+1566x^59+1797x^60+2388x^61+2178x^62+1996x^63+1661x^64+1446x^65+766x^66+446x^67+222x^68+88x^69+79x^70+24x^71+24x^72+10x^73+10x^74+1x^76+3x^78+1x^82

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 3.01 seconds.