The generator matrix

 1  0  1  1  1  1  1 2X^2+X  1  1  1 2X  1  1  1  1  1  1  1  1  1
 0  1 2X^2+2X+1  2 2X^2+X X+1 2X^2+X+2  1 2X 2X+2 2X^2+1  1 X+1 2X^2+1 2X^2+2X+1  0 2X^2+X 2X^2+1 2X^2+2X+1  0 X^2
 0  0 2X^2  0 2X^2 X^2 X^2 X^2  0  0 X^2  0 X^2 2X^2 2X^2  0 X^2 2X^2 X^2 2X^2 2X^2
 0  0  0 X^2 2X^2 2X^2 X^2  0 X^2 2X^2  0 2X^2 X^2  0 2X^2 2X^2  0 X^2  0  0 2X^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+62x^36+108x^37+156x^38+308x^39+1272x^40+480x^41+596x^42+2538x^43+468x^44+396x^45+126x^46+24x^47+4x^48+6x^49+6x^50+2x^51+6x^54+2x^60

The gray image is a linear code over GF(3) with n=189, k=8 and d=108.
This code was found by Heurico 1.16 in 0.0343 seconds.