The generator matrix

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

generates a code of length 30 over Z3[X]/(X^2) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+72x^57+18x^58+24x^59+24x^60+30x^61+24x^62+26x^63+6x^65+6x^66+6x^69+6x^70

The gray image is a linear code over GF(3) with n=90, k=5 and d=57.
This code was found by Heurico 1.16 in 0.00348 seconds.