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

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

Homogenous weight enumerator: w(x)=1x^0+130x^72+64x^73+384x^74+292x^75+910x^76+828x^77+1330x^78+1412x^79+1948x^80+1896x^81+1968x^82+1536x^83+1316x^84+812x^85+648x^86+276x^87+294x^88+48x^89+126x^90+4x^91+73x^92+50x^94+25x^96+6x^98+5x^100+1x^104+1x^112

The gray image is a code over GF(2) with n=648, k=14 and d=288.
This code was found by Heurico 1.16 in 8.46 seconds.