The generator matrix

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

generates a code of length 21 over Z3[X]/(X^3) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+36x^34+242x^36+168x^37+810x^38+770x^39+2820x^40+3240x^41+1514x^42+5400x^43+3240x^44+1034x^45+300x^46+50x^48+24x^49+14x^51+10x^54+8x^57+2x^60

The gray image is a linear code over GF(3) with n=189, k=9 and d=102.
This code was found by Heurico 1.16 in 39.9 seconds.