The generator matrix

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

generates a code of length 65 over Z16 who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+72x^57+421x^58+1006x^59+2394x^60+3078x^61+5596x^62+6552x^63+9617x^64+8480x^65+9466x^66+6406x^67+5678x^68+3036x^69+2079x^70+828x^71+461x^72+172x^73+92x^74+50x^75+19x^76+6x^77+9x^78+4x^79+5x^80+4x^81+1x^82+2x^83+1x^84

The gray image is a code over GF(2) with n=520, k=16 and d=228.
This code was found by Heurico 1.16 in 39.2 seconds.