The generator matrix

 1  0  1  1  1  6  1  1 12  1  1 10  0  1  1  1  1  6 12  1  1 10  1  1  1  6  1  1  1  1  0  1 10  1  1  1  2 12  1 10  1  0 12  6 12  1  4  1  1 12  1  6  1  1  1  1  1  1 14 12  4  1  1  1  1  6  0  1  2  2  0
 0  1  3  6  5  1 12 15  1 10  9  1  1  0  3  6  5  1  1 15 12  1  9 10  9  1  0  6 10 15  1 12  1  3 12  5  1  1  6  1 10  1  1  1  1  0  1  0 10  1  5  1  6  8  9  3 13  2  1  1  1 10  5  5  5  1  1 15  6  6  1
 0  0  8  0  0  0  0  0  0  8  0  0  0  8  8  8  8  8  8  8  0  8  8  8  0  8  8  0  0  0  0  8  8  8  8  8  0  8  8  0  0  8  8  8  8  8  0  8  0  8  8  0  8  8  0  0  0  0  0  0  8  0  8  8  0  0  0  8  8  0  0
 0  0  0  8  0  0  0  8  0  8  8  0  8  8  0  8  0  8  0  8  0  8  0  0  8  8  0  0  8  0  8  0  0  8  0  8  8  0  0  8  8  0  8  0  0  8  0  8  8  8  0  8  8  8  0  0  8  0  0  0  0  8  0  8  8  8  8  8  0  0  0
 0  0  0  0  8  0  0  0  8  0  8  0  8  0  0  0  0  8  8  8  0  0  8  0  0  0  0  8  8  8  0  8  8  0  8  8  8  0  8  8  8  8  8  0  8  8  8  0  0  0  8  0  8  8  0  8  8  0  0  0  0  0  0  8  8  0  0  8  0  0  0
 0  0  0  0  0  8  0  8  8  0  8  0  0  0  0  8  8  8  0  0  8  8  8  8  8  8  8  0  8  8  0  8  8  0  8  0  0  8  0  0  0  0  0  0  8  8  0  8  8  0  0  0  8  0  8  0  0  8  8  8  8  8  8  8  8  8  8  8  8  0  0
 0  0  0  0  0  0  8  8  0  8  8  8  8  0  8  8  0  0  8  0  8  8  8  0  0  0  8  8  8  0  0  0  0  0  8  8  0  8  0  8  8  0  0  8  8  8  0  8  0  8  8  0  0  0  8  0  0  8  8  0  0  8  8  0  0  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+52x^64+178x^65+226x^66+538x^67+492x^68+1218x^69+773x^70+1282x^71+765x^72+1174x^73+501x^74+542x^75+210x^76+182x^77+25x^78+6x^79+13x^80+7x^82+2x^84+1x^86+1x^88+1x^90+1x^94+1x^98

The gray image is a code over GF(2) with n=568, k=13 and d=256.
This code was found by Heurico 1.16 in 1.12 seconds.