The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  8  2  1  2  1  0  2  1  1  1  8  1  2  1  1  1  1 12  4  1  1  1  1  2  1  2 12  1  2  1  1  0  2  1  1  2  4  1  1  4  1  0  2
 0  2  0  6  0  6  8  2  4  4  6 14  4 12 10  2  0  6  4 10 14  2  6 12 14 12  2 14  2  6  0  2  2  2  4  0 12  6  2  2  6  2  4  8 10  4  2  2  2  6  6  2  2 10 10  4  0  4 12 12  8  0  4 12
 0  0 12  0  0  0 12  0 12  4  0  0  8  0  0  0  8  4  4  4 12 12  0  4  8  8  4  0  8 12 12  8  4  0  8 12  8  4  0  4  0  4  4  4 12  4  8 12  4  4  4  4  8  0  8  0  4  8 12  8 12  0 12  4
 0  0  0 12  0  0  0  4  8  8  4  8  8  8  4  0 12  4 12  0  0  4  8 12  8  4  0  4  0 12 12 12  4  0  0  8  4  8 12 12  4  4  4  8  0  8 12  0  8 12  8  0  8  4 12  8  4  0  8 12  8 12  0  8
 0  0  0  0 12  0  4  8  0  4  4 12  8  4 12 12  4  0 12  4  8 12  0  8 12  4 12  8  0  4  0  8  0  4  4  4  8  4  4  8 12  4 12  4  4  0 12  4  4  0  8 12  0  0  0 12 12  4 12  8  4  0 12  8
 0  0  0  0  0  8  0  8  8  8  0  8  8  8  8  0  0  0  0  8  8  0  0  0  8  8  8  0  0  8  8  8  8  0  8  8  8  0  0  8  8  0  8  0  0  0  0  0  0  0  0  0  8  8  0  0  0  0  0  8  8  8  0  0

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

Homogenous weight enumerator: w(x)=1x^0+196x^56+116x^57+518x^58+420x^59+1002x^60+1292x^61+1858x^62+1700x^63+2323x^64+1892x^65+1654x^66+1228x^67+956x^68+388x^69+414x^70+108x^71+155x^72+24x^73+80x^74+32x^76+16x^78+4x^80+4x^82+2x^84+1x^88

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 21.2 seconds.