The generator matrix

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

generates a code of length 61 over Z16 who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+37x^54+360x^55+1100x^56+1952x^57+2673x^58+3838x^59+4147x^60+4840x^61+4333x^62+3660x^63+2484x^64+1686x^65+845x^66+478x^67+183x^68+60x^69+42x^70+16x^71+19x^72+6x^73+6x^74+2x^76

The gray image is a code over GF(2) with n=488, k=15 and d=216.
This code was found by Heurico 1.16 in 9.52 seconds.