The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+123x^70+336x^71+764x^72+1324x^73+2067x^74+2656x^75+3281x^76+4004x^77+4107x^78+3784x^79+3383x^80+2748x^81+1699x^82+1056x^83+645x^84+348x^85+166x^86+104x^87+97x^88+24x^89+20x^90+14x^92+6x^94+7x^96+2x^98+2x^102

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 17 seconds.