The generator matrix

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

generates a code of length 27 over Z3[X]/(X^3) who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+54x^46+96x^47+62x^48+180x^49+204x^50+84x^51+234x^52+78x^53+4396x^54+162x^55+498x^56+22x^57+252x^58+66x^59+12x^60+90x^61+30x^62+2x^63+22x^66+12x^69+2x^72+2x^75

The gray image is a linear code over GF(3) with n=243, k=8 and d=138.
This code was found by Heurico 1.16 in 20.6 seconds.