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

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

Homogenous weight enumerator: w(x)=1x^0+123x^72+310x^73+712x^74+996x^75+1472x^76+1894x^77+2624x^78+3028x^79+3695x^80+3742x^81+3434x^82+2896x^83+2618x^84+1694x^85+1303x^86+778x^87+607x^88+338x^89+204x^90+128x^91+86x^92+48x^93+5x^94+14x^95+6x^96+6x^97+5x^98+1x^106

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 24.8 seconds.