The generator matrix

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

generates a code of length 81 over Z16 who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+232x^72+268x^73+934x^74+1396x^75+2521x^76+3628x^77+5276x^78+6220x^79+8150x^80+8636x^81+7890x^82+6416x^83+5292x^84+3692x^85+2302x^86+1136x^87+727x^88+264x^89+268x^90+60x^91+110x^92+24x^93+56x^94+4x^95+14x^96+8x^98+5x^100+2x^102+4x^104

The gray image is a code over GF(2) with n=648, k=16 and d=288.
This code was found by Heurico 1.16 in 86.1 seconds.