The generator matrix

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

generates a code of length 62 over Z16 who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+175x^54+152x^55+672x^56+784x^57+1759x^58+2456x^59+3817x^60+4280x^61+4671x^62+4336x^63+3876x^64+2432x^65+1643x^66+728x^67+494x^68+184x^69+153x^70+8x^71+82x^72+45x^74+17x^76+1x^78+1x^80+1x^82

The gray image is a code over GF(2) with n=496, k=15 and d=216.
This code was found by Heurico 1.16 in 16.5 seconds.