The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  3  0  0  0  3  3  3 3a 6a+3  0  3 3a 6a+6  0
 0  0  3  0  0 3a+6 6a+6 3a  6 3a+6  3 3a+6 3a 3a+3  0
 0  0  0  3  0 3a+6  3 3a+3 3a+3 6a+6 6a+3 6a+6 6a+3 6a  0
 0  0  0  0  3 6a+6  6 6a+3  3  3 3a 3a  3 3a+3  0

generates a code of length 15 over GR(81,9) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+336x^81+1584x^90+3576x^99+7960x^108+16056x^117+472392x^120+18168x^126+11368x^135

The gray image is a code over GF(9) with n=135, k=6 and d=81.
This code was found by Heurico 1.16 in 13.2 seconds.