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

generates a code of length 46 over Z3[X]/(X^3) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+102x^82+216x^83+84x^84+468x^85+444x^86+144x^87+510x^88+846x^89+3054x^90+528x^91+4212x^92+5976x^93+456x^94+1020x^95+108x^96+480x^97+342x^98+48x^99+228x^100+162x^101+34x^102+102x^103+48x^104+12x^105+36x^106+2x^108+6x^109+6x^111+6x^114+2x^129

The gray image is a linear code over GF(3) with n=414, k=9 and d=246.
This code was found by Heurico 1.16 in 2.13 seconds.