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 X^2  1  1  1  X  X 2X^2  1  1  1  1  1
 0  X 2X X^2 2X^2+X X^2+2X 2X^2 X^2+X 2X^2+2X  0 2X^2+X 2X X^2 X^2+X X^2+2X 2X^2  X 2X^2+2X  0 2X^2+X 2X X^2 X^2+X X^2+2X 2X^2+X 2X  X X^2+X X^2+2X  X 2X^2  X 2X^2+2X  X 2X^2+2X  X  0 X^2 2X^2  0 X^2

generates a code of length 41 over Z3[X]/(X^3) 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 linear code over GF(3) with n=369, k=5 and d=243.
This code was found by Heurico 1.16 in 0.0153 seconds.