The generator matrix

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

generates a code of length 30 over Z3[X]/(X^3) who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+120x^51+204x^52+312x^53+1304x^54+1104x^55+2310x^56+5292x^57+4446x^58+7836x^59+11320x^60+6618x^61+7788x^62+6858x^63+2052x^64+660x^65+480x^66+126x^67+48x^68+112x^69+18x^70+18x^72+12x^73+6x^75+4x^78

The gray image is a linear code over GF(3) with n=270, k=10 and d=153.
This code was found by Heurico 1.16 in 3.7 seconds.