The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+406x^72+1422x^73+3610x^74+4904x^75+7431x^76+10800x^77+14585x^78+14666x^79+16009x^80+14868x^81+14142x^82+10706x^83+7522x^84+4580x^85+2983x^86+1224x^87+733x^88+246x^89+123x^90+44x^91+23x^92+20x^93+12x^94+6x^95+2x^96+1x^98+2x^99+1x^104

The gray image is a code over GF(2) with n=640, k=17 and d=288.
This code was found by Heurico 1.16 in 199 seconds.