The generator matrix

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

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+306x^36+162x^38+390x^39+486x^40+648x^41+2142x^42+972x^43+648x^44+648x^45+132x^48+26x^54

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 38.9 seconds.