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

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+312x^83+260x^84+840x^86+570x^87+486x^88+1542x^89+1774x^90+1944x^91+3384x^92+3018x^93+1944x^94+1728x^95+576x^96+516x^98+190x^99+318x^101+122x^102+96x^104+42x^105+12x^107+6x^108+2x^120

The gray image is a linear code over GF(3) with n=414, k=9 and d=249.
This code was found by Heurico 1.16 in 1.4 seconds.