The generator matrix

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

generates a code of length 15 over Z3[X]/(X^2) who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+64x^21+120x^24+98x^27+486x^28+148x^30+972x^31+120x^33+126x^36+40x^39+12x^42

The gray image is a linear code over GF(3) with n=45, k=7 and d=21.
This code was found by Heurico 1.16 in 0.465 seconds.