The generator matrix

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

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+10x^27+60x^30+6x^33+2x^36+2x^45

The gray image is a linear code over GF(3) with n=45, k=4 and d=27.
This code was found by Heurico 1.16 in 0.000487 seconds.