The generator matrix

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

generates a code of length 20 over Z3[X]/(X^3) who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+64x^27+168x^30+224x^33+790x^36+2304x^39+13122x^40+2330x^42+334x^45+222x^48+92x^51+26x^54+6x^57

The gray image is a linear code over GF(3) with n=180, k=9 and d=81.
This code was found by Heurico 1.16 in 0.556 seconds.