The generator matrix

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

generates a code of length 20 over Z3[X]/(X^3) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+108x^34+96x^35+250x^36+144x^37+156x^38+202x^39+4806x^40+90x^41+76x^42+216x^43+102x^44+178x^45+72x^46+42x^47+20x^48+2x^60

The gray image is a linear code over GF(3) with n=180, k=8 and d=102.
This code was found by Heurico 1.16 in 1.89 seconds.