The generator matrix

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

generates a code of length 80 over Z16 who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+83x^72+408x^73+777x^74+1184x^75+2310x^76+2540x^77+3734x^78+3490x^79+4170x^80+3638x^81+3664x^82+2278x^83+1921x^84+1026x^85+668x^86+366x^87+220x^88+114x^89+71x^90+42x^91+26x^92+18x^93+8x^94+4x^96+5x^98+1x^100+1x^106

The gray image is a code over GF(2) with n=640, k=15 and d=288.
This code was found by Heurico 1.16 in 16.6 seconds.