The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+203x^72+618x^73+1419x^74+2808x^75+3869x^76+5724x^77+6435x^78+7786x^79+8083x^80+8200x^81+6499x^82+5282x^83+3593x^84+2492x^85+1205x^86+664x^87+286x^88+162x^89+108x^90+28x^91+20x^92+16x^93+12x^94+6x^95+7x^96+4x^97+2x^98+2x^99+2x^100

The gray image is a code over GF(2) with n=640, k=16 and d=288.
This code was found by Heurico 1.16 in 51.8 seconds.