The generator matrix

 1  0  1  1  1  6  1  1 12  1  1  6  1 10  1  0  1  1 10  1  1  1  1  8  1  2  1  4  1  1  1  8  4  1  1  1 12  1  1 14  1  4  1  1  6  1  1  1  1  1  1  1  4  1  1  1  6  1  2  1  8  0  1  1 12  1  2  1  1  1
 0  1 11  6 13  1  7  8  1  2 13  1  8  1  1  1 11 14  1  7 12  5 10  1  9  1  6  1 15  4 10  1  1  5  3  6  1 12  3  1 10  1  7 15  1  4  9  9  5  4 15  9  1  6 14  9  1 14 10 10  1  1  4  9  1  9  6 13  5  0
 0  0 12  0  4  0  4  4  0  0  8  4  8  4 12 12  8  4  8  8  4 12 12  0  4 12  0  0  0 12  8  8 12  8  4 12  4  8  8  4  4 12 12  0  0  0  0  4  8  4 12  4  4 12 12  0  0  4  8  4  8 12 12  0  8  8 12 12  8  0
 0  0  0 12  0  0  0  8  8 12 12 12 12  4  8  4 12  8  0 12 12  4  4  4  4  8  8  4  8  8  0  4  0  0 12  4 12  8  0  8  4  0  0 12 12  0  8  4 12  8  0  8 12  4  0  0  0  8  4  8  4  0  4  8  0 12  4 12  8  0
 0  0  0  0  8  0  8  8  8  8  0  8  0  8  0  0  8  8  8  8  8  8  8  8  8  0  0  0  8  0  8  0  8  0  0  0  0  8  8  8  0  0  8  0  8  8  8  0  8  8  8  8  0  0  8  0  8  0  0  0  8  0  8  0  8  8  8  0  0  0
 0  0  0  0  0  8  8  0  0  0  0  0  8  8  8  8  8  8  8  0  8  8  0  8  0  0  8  0  8  0  0  8  0  0  0  0  8  8  0  8  0  8  0  8  8  8  0  8  0  8  8  0  0  8  0  8  8  8  8  0  8  0  0  0  0  8  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+33x^62+116x^63+248x^64+646x^65+772x^66+1726x^67+1265x^68+2652x^69+1515x^70+2710x^71+1378x^72+1706x^73+660x^74+512x^75+161x^76+98x^77+76x^78+38x^79+11x^80+16x^81+8x^82+16x^83+5x^84+2x^85+7x^86+2x^88+2x^91+1x^92+1x^94

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 4.13 seconds.