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

generates a code of length 70 over Z16 who´s minimum homogenous weight is 61.

Homogenous weight enumerator: w(x)=1x^0+100x^61+348x^62+476x^63+1005x^64+1242x^65+2034x^66+2248x^67+3387x^68+3502x^69+3916x^70+3792x^71+3419x^72+2434x^73+2052x^74+978x^75+819x^76+414x^77+284x^78+102x^79+103x^80+44x^81+28x^82+14x^83+2x^84+8x^85+8x^86+6x^87+2x^90

The gray image is a code over GF(2) with n=560, k=15 and d=244.
This code was found by Heurico 1.16 in 22.2 seconds.