The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+293x^64+408x^65+669x^66+936x^67+1415x^68+1528x^69+2116x^70+2116x^71+1968x^72+1508x^73+1277x^74+696x^75+579x^76+288x^77+235x^78+148x^79+117x^80+44x^81+18x^82+8x^83+10x^84+5x^86+1x^104

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 6.08 seconds.