The generator matrix

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

generates a code of length 31 over Z3[X]/(X^3) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+12x^60+210x^62+8x^63+6x^66+6x^71

The gray image is a linear code over GF(3) with n=279, k=5 and d=180.
This code was found by Heurico 1.16 in 0.00564 seconds.