The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  1
 0  X  0  0 2X 2X^2+X 2X^2+2X  X 2X X^2 2X^2 X^2+X 2X X^2 X^2 X^2 2X X^2+X X^2 2X^2+2X 2X^2+X
 0  0  X 2X X^2 2X^2+2X X^2+X  X 2X^2+2X 2X^2 2X^2+X 2X^2+X 2X^2  0 2X^2+2X X^2+2X 2X^2 X^2+2X 2X^2+2X 2X^2+X 2X^2
 0  0  0 X^2  0  0 2X^2 X^2 2X^2 2X^2 2X^2 2X^2 X^2 X^2 2X^2  0 2X^2 2X^2 X^2 2X^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+144x^36+96x^37+180x^38+326x^39+798x^40+372x^41+2230x^42+1404x^43+342x^44+302x^45+84x^46+72x^47+146x^48+48x^49+6x^50+8x^51+2x^57

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 0.0601 seconds.