The generator matrix

 1  0  0  0  1  1  1  1  1  1 2X  1 X^2+2X 2X^2  1  1 X^2+X  0  1  1  1
 0  1  0  0 2X^2+2X 2X^2 X^2 2X^2+X 2X^2+1 2X+1  1 2X^2+X+1  1  1  1  X  1  1 X+1 X^2+2 X+2
 0  0  1  0 2X^2+2X+1 2X^2+2X 2X+1 X+2 2X^2+X+1 2X+2  2  X 2X^2+1 2X^2+X+2 2X^2+X+2 2X^2+X X^2+1 2X^2+2X+1 X^2+2X X^2+2X+2 2X^2
 0  0  0  1 2X^2+2X+2 2X^2+2X+1 X+1 X^2 2X^2+2X X^2+X+2 X+1 X^2+1 2X^2+X+2 X+2 X^2+1 2X^2+X+2 2X^2+X 2X^2+X+1 2X^2 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 34.

Homogenous weight enumerator: w(x)=1x^0+882x^34+1308x^35+4238x^36+9804x^37+21408x^38+22708x^39+66786x^40+71760x^41+85194x^42+122580x^43+73032x^44+30808x^45+16620x^46+3972x^47+146x^48+84x^49+78x^50+30x^51+2x^54

The gray image is a linear code over GF(3) with n=189, k=12 and d=102.
This code was found by Heurico 1.16 in 130 seconds.