The generator matrix

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

generates a code of length 11 over Z3[X]/(X^3) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+270x^16+1812x^18+1620x^19+5832x^20+6672x^21+22194x^22+11664x^23+6732x^24+2160x^25+86x^27+6x^30

The gray image is a linear code over GF(3) with n=99, k=10 and d=48.
This code was found by Heurico 1.16 in 0.699 seconds.