The generator matrix

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

generates a code of length 32 over Z3[X]/(X^3) who�s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+266x^57+428x^60+486x^62+494x^63+2916x^64+972x^65+498x^66+356x^69+106x^72+24x^75+8x^78+4x^84+2x^90

The gray image is a linear code over GF(3) with n=288, k=8 and d=171.
This code was found by Heurico 1.16 in 5.42 seconds.