The generator matrix

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

generates a code of length 30 over Z3[X]/(X^2) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+156x^56+118x^57+162x^59+36x^60+66x^62+54x^63+60x^65+20x^66+36x^68+12x^69+6x^71+2x^72

The gray image is a linear code over GF(3) with n=90, k=6 and d=56.
This code was found by Heurico 1.16 in 0.00608 seconds.