The generator matrix

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

generates a code of length 10 over Z3[X]/(X^2) who´s minimum homogenous weight is 11.

Homogenous weight enumerator: w(x)=1x^0+108x^11+276x^12+1404x^14+1872x^15+7884x^17+5730x^18+19332x^20+8124x^21+10260x^23+3636x^24+378x^26+20x^27+24x^30

The gray image is a linear code over GF(3) with n=30, k=10 and d=11.
This code was found by Heurico 1.16 in 0.988 seconds.