The generator matrix

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

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+60x^56+240x^57+36x^58+48x^59+28x^60+72x^61+20x^63+30x^64+48x^65+114x^66+6x^68+2x^78

The gray image is a linear code over GF(3) with n=90, k=6 and d=55.
This code was found by Heurico 1.16 in 0.00607 seconds.