The generator matrix

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

generates a code of length 30 over Z3[X]/(X^2) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+134x^54+108x^57+216x^60+234x^63+30x^72+6x^81

The gray image is a linear code over GF(3) with n=90, k=6 and d=54.
This code was found by Heurico 1.16 in 0.0967 seconds.