The generator matrix
1 1 1 1 1 1 1 1 1 1
0 X 2X X^2 2X^2+X X^2+2X 2X^2 X^2+X 2X^2+2X 0
generates a code of length 10 over Z3[X]/(X^3) who´s minimum homogenous weight is 18.
Homogenous weight enumerator: w(x)=1x^0+8x^18+216x^20+16x^21+2x^30
The gray image is a linear code over GF(3) with n=90, k=5 and d=54.
This code was found by Heurico 1.16 in 0.000249 seconds.