The generator matrix

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

generates a code of length 30 over Z3[X]/(X^3) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+30x^48+60x^50+108x^51+246x^52+240x^53+918x^54+696x^55+2832x^56+4948x^57+3558x^58+10560x^59+9808x^60+5532x^61+10560x^62+6568x^63+1464x^64+408x^65+82x^66+168x^67+126x^68+64x^69+46x^72+16x^75+10x^78

The gray image is a linear code over GF(3) with n=270, k=10 and d=144.
This code was found by Heurico 1.16 in 3.58 seconds.