The generator matrix

 1  0  1  1  1  6  1 12  1  1  1 10  1  1  8  1 14  1  1  1  4  1  1  2  1  1  0  1  6  1  1  1  0  6  1  1  1  1  1  4  2  4  1  1  2  1  1  1  2  4  1  1  1  1  1  1  1  1  1  1  1  2  1  8  1  1 10  1  1  1  1  1  1  0  1  1  1  8  1  0  1
 0  1 11  6  5  1  9  1 12  3 10  1 15  8  1 14  1 13  7  4  1  2  1  1  0  3  1  6  1 15 13  0  1  1  2 11  1  6  4  1  1  1  5  2  1  4  7  9  6  2  5 11 15  5 15 11  9  9 13  3 15  8  1  4  5 14  1 14  5  0  6  7 12  1  9  2  8  1  0  1  3
 0  0 12  0  0  8  0  8  8  8  8  0  8  4  4 12 12  4  4  4  4 12 12 12  0  8  0  0  0  8  4  4  4  4  4 12 12 12 12 12 12  0  8  0  0  0  4  8  8 12 12  8  0  8 12  4 12  4  0  4 12  4 12 12  8  0  0 12  4 12  8  4  0  4  0  8  4  8  8 12  0
 0  0  0  8  0  8  8  0  8  8  0  8  0  0  8  8  0  0  8  8  8  0  8  0  0  8  8  8  0  0  0  0  0  8  0  8  8  8  8  0  8  8  8  0  0  8  0  0  8  8  8  0  0  0  8  8  0  0  0  0  0  8  0  0  8  0  8  0  8  8  0  8  0  0  0  8  8  8  0  0  0
 0  0  0  0  8  8  8  8  8  0  8  0  0  0  8  0  8  8  0  8  0  8  8  0  8  8  8  8  8  8  0  8  0  8  0  8  0  8  0  8  0  0  0  0  0  0  8  0  0  8  8  8  8  0  0  0  0  0  0  8  8  8  8  8  8  8  8  0  8  8  8  8  0  8  8  0  8  0  8  0  0

generates a code of length 81 over Z16 who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+118x^76+356x^77+430x^78+590x^79+485x^80+446x^81+392x^82+404x^83+324x^84+262x^85+117x^86+106x^87+26x^88+6x^89+14x^90+4x^91+6x^92+2x^93+5x^94+1x^106+1x^114

The gray image is a code over GF(2) with n=648, k=12 and d=304.
This code was found by Heurico 1.16 in 0.789 seconds.