The generator matrix

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

generates a code of length 32 over Z3[X]/(X^3) who´s minimum homogenous weight is 61.

Homogenous weight enumerator: w(x)=1x^0+174x^61+48x^63+306x^64+24x^66+162x^67+4x^69+6x^70+2x^72+2x^78

The gray image is a linear code over GF(3) with n=288, k=6 and d=183.
This code was found by Heurico 1.16 in 0.0467 seconds.