The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  X  0  X  1  1  X
 0  X 2X  0 2X^2+X 2X X^2+2X X^2 2X^2+X 2X^2+X  0 2X 2X^2 X^2+2X  0 2X^2 2X^2+X X^2+X  0 2X 2X 2X^2+2X 2X^2+X 2X^2 X^2+2X 2X  X 2X^2+X 2X^2+2X X^2 2X^2+X
 0  0 X^2  0  0  0 2X^2  0 2X^2 2X^2 X^2 2X^2 2X^2 2X^2  0 2X^2 2X^2  0 X^2  0  0 2X^2 X^2  0 X^2 2X^2  0 2X^2 X^2  0 X^2
 0  0  0 X^2  0 X^2 2X^2 2X^2 2X^2 2X^2 2X^2  0 X^2 X^2  0 2X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0  0 X^2  0 2X^2 X^2  0
 0  0  0  0 2X^2 2X^2 X^2  0 2X^2 X^2 2X^2 2X^2 X^2  0 X^2 2X^2 X^2  0 X^2 2X^2 X^2 2X^2 2X^2 2X^2 X^2 2X^2 X^2 X^2  0 2X^2 X^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+112x^54+12x^55+126x^56+220x^57+78x^58+396x^59+1214x^60+180x^61+810x^62+2230x^63+168x^64+576x^65+162x^66+48x^67+36x^68+146x^69+22x^72+12x^75+8x^78+2x^81+2x^84

The gray image is a linear code over GF(3) with n=279, k=8 and d=162.
This code was found by Heurico 1.16 in 0.113 seconds.