The generator matrix

 1  0  1  1  1  1  1  1 2X^2  1  1  1  0  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1 X^2+X
 0  1  1  2 2X^2 2X^2+2  0 2X+1  1 X^2+2 2X^2+2X+2 2X^2+2X+1  1 2X^2+X X+2 2X+2 2X  X 2X^2+X 2X^2+X+2 2X^2+2X 2X+2 2X^2+X 2X^2+2 2X^2+2 2X^2+X+1 X^2+X 2X^2+X  1  1
 0  0 2X X^2  X 2X^2+X X^2+2X  X  X 2X^2 2X^2+X  0 2X 2X^2+2X X^2+X 2X X^2  X  0 2X^2 2X^2+X X^2 X^2+2X 2X X^2+2X  X 2X^2+X 2X X^2+X X^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+606x^56+780x^57+504x^58+948x^59+990x^60+720x^61+924x^62+702x^63+72x^64+240x^65+22x^66+24x^68+12x^69+12x^71+2x^72+2x^75

The gray image is a linear code over GF(3) with n=270, k=8 and d=168.
This code was found by Heurico 1.16 in 55.7 seconds.