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 X X 0 X X X^2 X X 2X^2 1 1 1 1 1 1 1 1 1 X X 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^2+2X 2X^2+X 2X X X^2+X X^2+2X X X 2X^2+2X X 0 X^2 2X^2 2X^2+X X^2+X X 2X X^2+2X 2X^2+2X 0 X^2 2X X^2+2X
generates a code of length 49 over Z3[X]/(X^3) who´s minimum homogenous weight is 97.
Homogenous weight enumerator: w(x)=1x^0+36x^97+162x^98+14x^99+18x^100+6x^102+4x^105+2x^114
The gray image is a linear code over GF(3) with n=441, k=5 and d=291.
This code was found by Heurico 1.16 in 0.0296 seconds.