The generator matrix

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

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+306x^34+348x^35+1746x^36+3276x^37+5814x^38+8796x^39+22548x^40+21264x^41+32154x^42+41184x^43+21288x^44+11688x^45+5454x^46+828x^47+258x^48+132x^49+30x^50+30x^51+2x^54

The gray image is a linear code over GF(3) with n=189, k=11 and d=102.
This code was found by Heurico 1.16 in 15.9 seconds.