The generator matrix

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

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+60x^15+714x^16+384x^17+4318x^18+3642x^19+24822x^20+16454x^21+55260x^22+48996x^23+16668x^24+4974x^25+642x^26+160x^27+48x^28+4x^30

The gray image is a linear code over GF(3) with n=99, k=11 and d=45.
This code was found by Heurico 1.16 in 5.53 seconds.