The generator matrix

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

generates a code of length 21 over Z3[X]/(X^3) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+236x^36+324x^37+912x^38+1164x^39+2028x^40+3144x^41+3118x^42+3474x^43+3132x^44+1468x^45+414x^46+96x^47+84x^48+78x^49+6x^50+2x^51+2x^54

The gray image is a linear code over GF(3) with n=189, k=9 and d=108.
This code was found by Heurico 1.16 in 0.294 seconds.