The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+55x^72+150x^73+310x^74+592x^75+913x^76+1354x^77+1921x^78+2050x^79+1865x^80+2026x^81+1888x^82+1312x^83+872x^84+532x^85+272x^86+116x^87+54x^88+28x^89+17x^90+10x^91+11x^92+6x^93+2x^94+14x^95+4x^96+4x^98+2x^99+1x^104+1x^106+1x^110

The gray image is a code over GF(2) with n=640, k=14 and d=288.
This code was found by Heurico 1.16 in 4.83 seconds.