The generator matrix

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

generates a code of length 15 over Z3[X]/(X^2) who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+76x^27+100x^30+48x^33+16x^36+2x^39

The gray image is a linear code over GF(3) with n=45, k=5 and d=27.
This code was found by Heurico 1.16 in 0.00076 seconds.