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

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

Homogenous weight enumerator: w(x)=1x^0+100x^72+374x^73+608x^74+1008x^75+1362x^76+2020x^77+2405x^78+3504x^79+3039x^80+4302x^81+3075x^82+3512x^83+2343x^84+1890x^85+1109x^86+776x^87+477x^88+322x^89+207x^90+148x^91+91x^92+46x^93+17x^94+10x^95+11x^96+6x^97+2x^98+2x^103+1x^110

The gray image is a code over GF(2) with n=648, k=15 and d=288.
This code was found by Heurico 1.16 in 24.5 seconds.