The generator matrix

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

generates a code of length 64 over Z16 who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+59x^56+198x^57+657x^58+916x^59+1788x^60+2684x^61+3379x^62+4704x^63+4182x^64+4756x^65+3496x^66+2536x^67+1573x^68+802x^69+496x^70+212x^71+186x^72+68x^73+26x^74+12x^75+19x^76+2x^77+8x^78+4x^79+2x^81+1x^82+1x^86

The gray image is a code over GF(2) with n=512, k=15 and d=224.
This code was found by Heurico 1.16 in 12.9 seconds.