The generator matrix

 1  0  1  1  1  1  1 2X^2+X  1  1  1 2X  1  1  1  0  1  1  1 2X^2+X  1  1  1 X^2  1 X^2+X  X  1  1  1  1 2X^2
 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 X+1 2X^2+X+2  1 2X X^2+1 X^2+2  1 X^2+X+2  1  X X^2 X^2+2X X^2+X X^2+2  1
 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 X^2  0 2X^2 2X^2 X^2  0 2X^2 2X^2  0  0 X^2 X^2 2X^2  0 X^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+480x^61+336x^62+8x^63+456x^64+342x^65+10x^66+456x^67+72x^68+6x^69+12x^70+6x^71+2x^75

The gray image is a linear code over GF(3) with n=288, k=7 and d=183.
This code was found by Heurico 1.16 in 5.15 seconds.