The generator matrix

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

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+678x^83+1522x^84+2898x^85+4752x^86+6438x^87+9198x^88+12462x^89+14446x^90+20358x^91+23592x^92+20278x^93+22374x^94+16152x^95+10464x^96+6192x^97+3150x^98+1384x^99+216x^100+282x^101+106x^102+138x^104+36x^105+30x^107

The gray image is a linear code over GF(3) with n=414, k=11 and d=249.
This code was found by Heurico 1.16 in 63.8 seconds.