The generator matrix

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

generates a code of length 32 over Z3[X]/(X^3) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+192x^60+162x^61+144x^62+582x^63+162x^64+144x^65+552x^66+162x^67+36x^68+42x^69+6x^75+2x^81

The gray image is a linear code over GF(3) with n=288, k=7 and d=180.
This code was found by Heurico 1.16 in 0.0131 seconds.