The generator matrix

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

generates a code of length 31 over Z3[X]/(X^3) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+96x^53+390x^54+558x^55+480x^56+1466x^57+3336x^58+3168x^59+5556x^60+11406x^61+5232x^62+7552x^63+11286x^64+3930x^65+3032x^66+966x^67+162x^68+150x^69+132x^70+54x^71+52x^72+18x^73+20x^75+6x^81

The gray image is a linear code over GF(3) with n=279, k=10 and d=159.
This code was found by Heurico 1.16 in 4.41 seconds.