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

generates a code of length 81 over Z16 who´s minimum homogenous weight is 71.

Homogenous weight enumerator: w(x)=1x^0+138x^71+490x^72+798x^73+1152x^74+1948x^75+2380x^76+3508x^77+5189x^78+6022x^79+7285x^80+7786x^81+7249x^82+6522x^83+4934x^84+3454x^85+2447x^86+1542x^87+1134x^88+682x^89+331x^90+280x^91+118x^92+52x^93+45x^94+26x^95+10x^96+6x^97+2x^99+2x^101+2x^102+1x^110

The gray image is a code over GF(2) with n=648, k=16 and d=284.
This code was found by Heurico 1.16 in 90.3 seconds.