The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1
 0 X^2  0  0  0  0 X^2 2X^2 2X^2  0  0 X^2 X^2 X^2 X^2 X^2  0 2X^2  0 2X^2 X^2
 0  0 X^2  0  0 X^2 2X^2  0 2X^2  0 X^2 X^2 2X^2 2X^2 X^2 X^2 X^2 X^2 X^2 2X^2 2X^2
 0  0  0 X^2  0 2X^2 2X^2 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0 2X^2  0 2X^2
 0  0  0  0 X^2 2X^2 2X^2 2X^2 2X^2 2X^2  0 2X^2  0  0 2X^2  0 2X^2  0 2X^2 X^2 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+86x^36+26x^39+162x^40+1496x^42+324x^43+38x^45+20x^48+14x^51+10x^54+8x^57+2x^60

The gray image is a linear code over GF(3) with n=189, k=7 and d=108.
This code was found by Heurico 1.16 in 0.0445 seconds.