The generator matrix

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

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+858x^53+1406x^54+4698x^55+9030x^56+11990x^57+25878x^58+35922x^59+48426x^60+73326x^61+79752x^62+78924x^63+75420x^64+48192x^65+21248x^66+11526x^67+4002x^68+516x^69+132x^70+120x^71+48x^72+18x^73+8x^75

The gray image is a linear code over GF(3) with n=279, k=12 and d=159.
This code was found by Heurico 1.16 in 215 seconds.