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  X  X  0  X  X  3  1  1  1  X  X  6  1  1  1  1  1
 0  X 2X  3 X+6 2X+3  6 X+3 2X+6  0 X+6 2X  3 X+3 2X+3  6  X 2X+6  0 X+6 2X  3 X+3 2X+3 X+6 2X  X X+3 2X+3  X  6  X 2X+6  X 2X+6  X  0  3  6  0  3

generates a code of length 41 over Z9[X]/(X^2+6,3X) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+14x^81+216x^82+6x^84+6x^96

The gray image is a code over GF(3) with n=369, k=5 and d=243.
This code was found by Heurico 1.16 in 0.0155 seconds.