The generator matrix

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

generates a code of length 44 over Z3[X]/(X^3) who´s minimum homogenous weight is 83.

Homogenous weight enumerator: w(x)=1x^0+210x^83+392x^84+738x^85+1224x^86+516x^87+792x^88+684x^89+384x^90+738x^91+600x^92+222x^93+12x^95+14x^99+18x^101+10x^102+6x^104

The gray image is a linear code over GF(3) with n=396, k=8 and d=249.
This code was found by Heurico 1.16 in 0.0986 seconds.