The generator matrix

 1  0  0  1  1  1 2X  1  1  1  1  1 2X^2+X  1  1 2X^2+2X  1  0  1  1  1
 0  1  0 2X^2+2X  1 2X^2+2X+1  1  0 2X^2+2 2X+2  2 2X  1 2X^2+2X+1 X+1  1 2X^2+X+2  1 X^2+X+1 2X^2+2X+2 X+1
 0  0  1 2X^2+2X+1  1 2X^2+2X+2 X+1  2 2X^2+X X+1  2 X^2+2X X^2+X+1 X^2+X+1 X^2 2X^2+X+2 2X^2 2X X^2+2X  0 2X+2
 0  0  0 2X^2 2X^2 2X^2  0 X^2  0 X^2 2X^2 X^2 X^2  0  0 X^2 X^2 2X^2 2X^2 X^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+790x^36+942x^37+1986x^38+4302x^39+5490x^40+7188x^41+13730x^42+10206x^43+7218x^44+5560x^45+1308x^46+120x^47+148x^48+36x^49+12x^50+10x^51+2x^57

The gray image is a linear code over GF(3) with n=189, k=10 and d=108.
This code was found by Heurico 1.16 in 1.97 seconds.