The generator matrix

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

generates a code of length 11 over Z3[X]/(X^3) who´s minimum homogenous weight is 15.

Homogenous weight enumerator: w(x)=1x^0+132x^15+162x^16+1266x^18+972x^19+10206x^20+4536x^21+15066x^22+20412x^23+4866x^24+1296x^25+110x^27+24x^33

The gray image is a linear code over GF(3) with n=99, k=10 and d=45.
This code was found by Heurico 1.16 in 23.2 seconds.