The generator matrix

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

generates a code of length 31 over Z3[X]/(X^3) who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+76x^51+138x^53+224x^54+552x^56+330x^57+486x^58+1848x^59+1818x^60+1944x^61+3336x^62+3390x^63+1944x^64+2418x^65+390x^66+420x^68+192x^69+36x^71+78x^72+36x^75+20x^78+6x^81

The gray image is a linear code over GF(3) with n=279, k=9 and d=153.
This code was found by Heurico 1.16 in 0.884 seconds.