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  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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0 12  0 12  0 12  0 12  0 12  0 12  0 12  0 12  0 12  0 12  0 12  0 12  0 12  0 12  0 12  8  4  8  4  8  4  4  8  8  4  8  4  8  4  0 12  8  4  8  4  8  4  8  4  8  4  8  4  8  4  8  4  8  4 12  0 12  0 12  0 12  4  0 12 12  4  4  0  8 12 12
 0  0  8  0  0  0  8  0  0  0  0  0  8  0  8  0  0  8  0  8  0  8  0  8  8  8  8  8  8  8  8  8  8  8  8  8  8  8  8  8  8  8  8  8  8  8  0  0  0  0  0  0  8  8  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  8  8  0  8  0  0  8  8  8  8  8
 0  0  0  8  0  0  0  8  0  0  0  0  0  8  0  8  8  8  8  8  8  8  8  8  8  0  8  0  8  0  8  0  0  0  0  0  0  0  0  8  8  8  8  8  8  0  8  8  8  8  8  8  8  8  8  8  0  0  0  0  0  0  0  0  0  0  0  0  8  0  8  0  8  8  8  8  0  8  0  8  0
 0  0  0  0  8  0  8  0  0  8  8  8  8  8  0  8  8  0  8  0  0  8  0  8  0  8  0  8  8  0  8  0  0  0  0  8  8  8  8  8  8  8  0  0  8  0  0  0  0  0  8  8  0  0  8  8  8  8  8  8  0  0  0  0  0  0  0  8  8  8  0  8  8  0  0  0  8  8  0  8  0
 0  0  0  0  0  8  0  8  8  8  8  0  8  0  8  8  0  0  8  8  8  8  0  0  0  0  8  8  8  8  0  0  0  8  8  8  0  8  0  0  8  8  8  8  0  0  0  0  8  8  8  8  0  0  0  0  0  0  8  8  8  8  0  0  0  0  8  8  0  0  0  8  8  8  8  0  0  8  8  0  0

generates a code of length 81 over Z16 who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+32x^77+16x^78+126x^80+704x^81+96x^82+32x^85+16x^86+1x^160

The gray image is a code over GF(2) with n=648, k=10 and d=308.
This code was found by Heurico 1.16 in 0.798 seconds.