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

generates a code of length 32 over Z3[X]/(X^3) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+180x^58+264x^59+96x^60+222x^61+966x^62+308x^63+2178x^64+1362x^65+306x^66+162x^67+132x^68+12x^69+120x^70+186x^71+4x^72+36x^73+6x^74+18x^76+2x^90

The gray image is a linear code over GF(3) with n=288, k=8 and d=174.
This code was found by Heurico 1.16 in 0.115 seconds.