The generator matrix

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

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+904x^54+990x^55+3258x^56+5118x^57+7272x^58+11700x^59+18948x^60+19710x^61+27486x^62+32528x^63+19854x^64+16452x^65+8022x^66+3204x^67+882x^68+672x^69+146x^72

The gray image is a linear code over GF(3) with n=279, k=11 and d=162.
This code was found by Heurico 1.16 in 31.8 seconds.