The generator matrix

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

generates a code of length 20 over Z3[X]/(X^3) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+642x^32+1356x^33+4506x^34+8034x^35+20066x^36+23718x^37+66162x^38+69634x^39+95286x^40+121002x^41+70978x^42+32268x^43+14052x^44+3378x^45+222x^46+60x^47+62x^48+6x^49+8x^51

The gray image is a linear code over GF(3) with n=180, k=12 and d=96.
This code was found by Heurico 1.16 in 121 seconds.