The generator matrix
1 1 1 1 1 1 1 1 1 1
0 X 0 2X^2+X 0 X 2X 2X^2+2X 2X 0
0 0 X X^2+2X 2X X 0 2X^2+X 2X 0
0 0 0 X^2 0 2X^2 0 X^2 2X^2 0
0 0 0 0 X^2 X^2 2X^2 X^2 X^2 0
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+92x^12+144x^14+336x^15+864x^17+480x^18+15336x^20+608x^21+1152x^23+636x^24+32x^27+2x^30
The gray image is a linear code over GF(3) with n=90, k=9 and d=36.
This code was found by Heurico 1.16 in 0.0939 seconds.