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.