The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+172x^54+564x^55+1220x^56+1962x^57+3080x^58+4948x^59+7396x^60+8176x^61+10182x^62+8968x^63+7333x^64+4690x^65+3093x^66+1828x^67+974x^68+490x^69+251x^70+76x^71+64x^72+36x^73+19x^74+2x^76+6x^77+3x^78+2x^80

The gray image is a code over GF(2) with n=496, k=16 and d=216.
This code was found by Heurico 1.16 in 45.6 seconds.