The generator matrix

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

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+270x^15+618x^18+864x^21+432x^24+2x^27

The gray image is a linear code over GF(3) with n=30, k=7 and d=15.
This code was found by Heurico 1.13 in 0.00322 seconds.