The generator matrix

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

generates a code of length 10 over Z3[X]/(X^2) who´s minimum homogenous weight is 15.

Homogenous weight enumerator: w(x)=1x^0+40x^15+54x^16+42x^17+122x^18+24x^19+78x^20+174x^21+60x^22+42x^23+62x^24+24x^25+6x^27

The gray image is a linear code over GF(3) with n=30, k=6 and d=15.
This code was found by Heurico 1.16 in 0.00113 seconds.