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

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

Homogenous weight enumerator: w(x)=1x^0+270x^72+204x^73+782x^74+776x^75+1454x^76+1696x^77+2480x^78+3364x^79+3377x^80+4348x^81+3228x^82+3280x^83+2406x^84+1840x^85+1344x^86+612x^87+597x^88+224x^89+244x^90+32x^91+103x^92+8x^93+68x^94+10x^96+14x^98+5x^100+1x^112

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 87.3 seconds.