The generator matrix

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

generates a code of length 31 over Z3[X]/(X^3) who´s minimum homogenous weight is 61.

Homogenous weight enumerator: w(x)=1x^0+60x^61+144x^62+30x^64+2x^66+4x^69+2x^75

The gray image is a linear code over GF(3) with n=279, k=5 and d=183.
This code was found by Heurico 1.16 in 0.00555 seconds.