The generator matrix

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

generates a code of length 31 over Z3[X]/(X^3) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+90x^54+126x^55+270x^56+220x^57+1470x^58+1404x^59+262x^60+5082x^61+2754x^62+274x^63+5184x^64+1836x^65+218x^66+276x^67+54x^68+110x^69+12x^70+20x^72+12x^75+6x^78+2x^81

The gray image is a linear code over GF(3) with n=279, k=9 and d=162.
This code was found by Heurico 1.16 in 0.494 seconds.