The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+138x^70+284x^71+750x^72+1104x^73+2018x^74+2756x^75+3564x^76+3680x^77+4208x^78+4144x^79+3483x^80+2576x^81+1808x^82+964x^83+648x^84+272x^85+128x^86+76x^87+75x^88+16x^89+42x^90+18x^92+10x^94+3x^96+1x^100+1x^108

The gray image is a code over GF(2) with n=624, k=15 and d=280.
This code was found by Heurico 1.16 in 16.8 seconds.