The generator matrix

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

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+538x^54+126x^55+738x^56+2184x^57+2178x^58+2610x^59+7650x^60+7452x^61+7182x^62+12848x^63+7218x^64+4014x^65+2976x^66+522x^67+36x^68+648x^69+122x^72+6x^75

The gray image is a linear code over GF(3) with n=279, k=10 and d=162.
This code was found by Heurico 1.16 in 33.8 seconds.