The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+116x^56+120x^57+246x^58+664x^59+591x^60+1736x^61+1274x^62+2808x^63+1352x^64+2904x^65+1031x^66+1800x^67+658x^68+600x^69+228x^70+104x^71+88x^72+16x^73+23x^74+5x^76+8x^78+3x^80+3x^82+2x^84+2x^86+1x^90

The gray image is a code over GF(2) with n=512, k=14 and d=224.
This code was found by Heurico 1.16 in 3.71 seconds.