The generator matrix

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

generates a code of length 71 over Z16 who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+54x^64+282x^65+608x^66+1008x^67+1395x^68+2008x^69+2009x^70+2084x^71+1903x^72+1880x^73+1303x^74+772x^75+484x^76+282x^77+125x^78+86x^79+32x^80+26x^81+15x^82+16x^83+2x^85+2x^86+2x^87+2x^88+2x^90+1x^92

The gray image is a code over GF(2) with n=568, k=14 and d=256.
This code was found by Heurico 1.16 in 4.01 seconds.