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

generates a code of length 30 over Z3[X]/(X^3) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+210x^56+108x^57+162x^58+378x^59+540x^60+324x^61+282x^62+42x^63+60x^65+36x^66+36x^68+6x^71+2x^81

The gray image is a linear code over GF(3) with n=270, k=7 and d=168.
This code was found by Heurico 1.16 in 0.0475 seconds.