The generator matrix

 1  0  0  0  1  1  1  1  8  1  2  4  1  1  0 10 10  1  6  4  1  1  1  1  1  2 10  1  4  1 10  4  1 10  1  8  0  8  2  1  1  1  1  4  0 10  1  4  2  1  2  1  2  1  1  1  4  1  1  1  1  1  1 14 12 10  1 14  1 14 12  8  1  1 14  1  1  1
 0  1  0  0  2  5  8 13  1  3  1 14 10 15  1  2  1  3 12  1  0 15  2 11 14  1 12  9  1  1  1  4 14 10 11  1  1  1  8 11 10 14 12  1  6  1  6 10  4  1  1 14  6  7  8  9  8  3  9  0  2  4  0  1  0  1  3 14 10  1  1  1  0  0 10  3  2  8
 0  0  1  0  0  8 13  5  1  5 15  1  1  4  4  1  1 15  1 15  6  4  3  2  8  2 10 11 14  9  8  1 11 14  1 15  9 11  1  7 10 10 15  0  1  4  5 12  1 12  0 14  1 14 12  7  1  6 10  0  5 15 12 10  2  2  1  4  5 11  1  2  2  9  1  2  7  0
 0  0  0  1  1 11  3  6  7  5  0 13 12 10 11  2  8 13 13 13  3  1 15  6  0  3  1  1  4  8  6 14  6  1 10  2 13 12 11  3 13  0 15 12  8  9 10  1  0 12 15 15  7 10  2  3 15  0 15 10 12  0  9  5  1  7 13  1 15  3  0 13 10  4 11 10  3  4
 0  0  0  0  8  0  0  0  0  8  8  8  8  8  8  0  8  8  8  0  8  0  0  8  0  8  0  8  0  0  8  8  8  8  8  0  8  8  0  0  0  8  0  8  0  8  0  8  0  0  8  8  8  0  0  0  8  8  8  8  0  8  0  0  0  0  0  0  8  8  0  0  8  8  0  8  8  8

generates a code of length 78 over Z16 who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+314x^70+1476x^71+3172x^72+4902x^73+7894x^74+10586x^75+14134x^76+14686x^77+17275x^78+14898x^79+14101x^80+9966x^81+7871x^82+4796x^83+2656x^84+1332x^85+507x^86+262x^87+142x^88+56x^89+23x^90+14x^91+2x^92+2x^93+4x^94

The gray image is a code over GF(2) with n=624, k=17 and d=280.
This code was found by Heurico 1.16 in 194 seconds.