The generator matrix

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

generates a code of length 31 over Z3[X]/(X^3) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+60x^62+2x^63+12x^65+6x^66

The gray image is a linear code over GF(3) with n=279, k=4 and d=186.
This code was found by Heurico 1.16 in 0.00543 seconds.