The generator matrix

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

generates a code of length 10 over Z3[X]/(X^3) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+60x^12+144x^15+546x^18+4374x^20+1212x^21+180x^24+20x^27+24x^30

The gray image is a linear code over GF(3) with n=90, k=8 and d=36.
This code was found by Heurico 1.16 in 0.0133 seconds.