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

generates a code of length 70 over Z16 who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+144x^62+156x^63+432x^64+548x^65+1115x^66+1228x^67+1643x^68+2236x^69+1842x^70+2196x^71+1440x^72+1124x^73+848x^74+452x^75+450x^76+180x^77+178x^78+64x^79+46x^80+8x^81+29x^82+19x^84+4x^86+1x^96

The gray image is a code over GF(2) with n=560, k=14 and d=248.
This code was found by Heurico 1.16 in 5.85 seconds.