The generator matrix

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

generates a code of length 79 over Z16 who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+105x^72+680x^73+1380x^74+2280x^75+2841x^76+3742x^77+3738x^78+4330x^79+3338x^80+3634x^81+2281x^82+1878x^83+1199x^84+604x^85+316x^86+200x^87+116x^88+34x^89+34x^90+14x^91+10x^93+10x^94+2x^95+1x^98

The gray image is a code over GF(2) with n=632, k=15 and d=288.
This code was found by Heurico 1.16 in 13.4 seconds.