The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+44x^62+86x^63+185x^64+310x^65+452x^66+604x^67+864x^68+1088x^69+1067x^70+1078x^71+837x^72+552x^73+425x^74+254x^75+145x^76+82x^77+35x^78+14x^79+13x^80+14x^81+13x^82+10x^83+3x^84+2x^85+10x^86+2x^87+1x^90+1x^106

The gray image is a code over GF(2) with n=560, k=13 and d=248.
This code was found by Heurico 1.16 in 1.81 seconds.