The generator matrix

 1  0  1  1  1  4  1  1  6  1  1  4  2  1  1  1  1 10  1  4  1  1  1 14 12  1  1  1  1  1 12  1  1  1  6  0 10  1  1  1  2  1  1  1  1  4  1  1  1 12  1  1  1  2  8  1  8 12 10  1  4  8  1  1  1  0  2 12  1 12  2  1  2  1  2  2  1  8  0  4  1
 0  1  1  0  3  1  5  4  1 12 15  1  1 14 15  5  2  1  7  1 14  6  5  1  1  3  2  4  9  3  1  0 13 11  1  1  1 15  6 14  1 11  1  2  8  1  8  8  2  1  7  6  9  4  1 11  1  2  1  8  1  2 10 11  7 12 12  1  2  8  0  6  2 15  6  4  3  4  8  2  0
 0  0  2  0  0  0  2 10  6  2  8 14  0  8  2  4  6  2  6  6  0 14 12  8  4  4  2  4  6 10  6  2  2 10  8  8  6  0 12  0 12 12 12 10  6  4  0  6  0 10  8 12  4 14  0  2 12  6  2  4 10  6 12 14 14  2 14 12  4  2 10 14  2 14  2 14  0  8  2  0 12
 0  0  0  2  0  2  2  8 14  6 14 12 10  4 10  0  4  4 12  2  6 14  2 12 10 10  8  0  0 12  0  6 14  6  8  4  6  2  2  8  2  8  4 14  8  8 10 10  8  6 14 14 12 12  6  2  6  4  0 14 14  6  6  8 14  6  4 12  0 12  0  4  4  0  6  2  2  2 14  2 12
 0  0  0  0  8  0  0  8  8  8  8  8  0  0  0  8  8  8  0  8  0  8  0  8  8  8  0  8  8  8  0  0  8  8  8  0  0  0  8  8  8  0  0  8  0  8  8  0  8  0  0  8  0  8  0  8  0  0  8  8  8  0  0  0  8  8  0  0  8  8  8  0  0  0  0  0  8  0  0  8  0
 0  0  0  0  0  8  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  8  0  0  0  8  8  0  8  0  0  0  0  8  8  8  0  8  8  8  8  8  0  0  0  8  0  8  0  8  0  0  8  8  0  0  0  0  0  8  0  8  0  8  8  8  0  0  8  8  8  0  8  0  0  8  8  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+123x^72+514x^73+1057x^74+1870x^75+2829x^76+3636x^77+5543x^78+5948x^79+7592x^80+7214x^81+7813x^82+6320x^83+5461x^84+3662x^85+2734x^86+1374x^87+776x^88+470x^89+277x^90+150x^91+70x^92+42x^93+15x^94+18x^95+12x^96+14x^97+1x^98

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 64 seconds.