The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  8  2  2  0  8  1  1  2  1  0  0  0  2  2  2  1  4  2  1  8  1  0  1  1  2  1  1  1  0  4  2  2  2 12  2  1  1  1  1  1  1
 0  2  0  0  0  0  0  0  0 10  6 10 14 10  2  2  8  4 12  8  6  6 10  2  4  6  4  2 10 12  4 14  0 12  0 10 14  2  0  2  2  2 10  8  2  0  6  4  6  0  4  8  4  2 10  8  2  2  8 12  8  4  0  6 14 14 10  2  8  4  2 14  4  4  0  0 10  2  2  4 12  8
 0  0  2  0  0  8 10  6  6  2  6  0  2  0  8 14 10  0  8  2 14 12  4  8  2  8  0  6  2 10 12  6  6 12  8 12  6  6  4 10 14  8  6  2  8  2  2  4  4  6  2  0  2 12  2  2 14 12  4  4  2 14  4 10  0 14  2  8 12 12 14  0 10  0  8  4 14 10 10  6 12  8
 0  0  0  2  0 10 10 10  8  2 14  8  4 10 10  8 14 10  8 12  2  0 14  0 14  6  2  8  2 12 12  4  4  8  6  4  0  4  4 14 14 14  8  2 12  0 14 10  0  6 10  2 14  2 10  4 10 12  8 10  8  6  2  4 10  4  6  4 12  2  0 10 12  8  8 14 12  8  2  0 14  0
 0  0  0  0  2  2  8 10  2 14  8 14  2  2  4 12 12 10  2  6 10  8 12  2 14  2 12 10  4  4  0  4  0  8  6  6  4 14 10  8 12 10  8  4  4  2  8 12 14  2  6  8  0  0 10  0  2  2 14 14 12 10  0  4  0  8  4  4 12 14  0  8 10  6  2  2 12  0 12  2  2  0

generates a code of length 82 over Z16 who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+81x^72+462x^73+764x^74+1400x^75+1675x^76+2662x^77+3339x^78+5284x^79+5860x^80+7424x^81+7506x^82+8232x^83+5754x^84+5018x^85+3309x^86+2490x^87+1521x^88+1186x^89+569x^90+436x^91+247x^92+164x^93+60x^94+46x^95+25x^96+12x^97+4x^98+4x^100+1x^114

The gray image is a code over GF(2) with n=656, k=16 and d=288.
This code was found by Heurico 1.16 in 91.7 seconds.