The generator matrix

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

generates a code of length 64 over Z16 who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+86x^57+219x^58+436x^59+872x^60+1414x^61+1882x^62+2194x^63+2313x^64+2192x^65+1856x^66+1364x^67+831x^68+402x^69+157x^70+64x^71+31x^72+6x^73+6x^74+16x^75+11x^76+12x^77+6x^78+6x^79+4x^80+1x^82+1x^86+1x^88

The gray image is a code over GF(2) with n=512, k=14 and d=228.
This code was found by Heurico 1.16 in 3.92 seconds.