The generator matrix

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

generates a code of length 30 over Z3[X]/(X^2) who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+24x^55+24x^57+36x^58+28x^60+72x^61+20x^63+30x^64+6x^66+2x^78

The gray image is a linear code over GF(3) with n=90, k=5 and d=55.
This code was found by Heurico 1.16 in 0.187 seconds.