The generator matrix

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

generates a code of length 46 over Z3[X]/(X^3) who´s minimum homogenous weight is 83.

Homogenous weight enumerator: w(x)=1x^0+480x^83+524x^84+594x^85+1878x^86+2142x^87+2826x^88+4728x^89+4768x^90+6714x^91+7320x^92+6902x^93+7344x^94+5634x^95+3360x^96+1440x^97+1356x^98+382x^99+36x^100+348x^101+134x^102+102x^104+6x^105+18x^107+6x^108+6x^110

The gray image is a linear code over GF(3) with n=414, k=10 and d=249.
This code was found by Heurico 1.16 in 7.4 seconds.