The generator matrix

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

generates a code of length 44 over Z3[X]/(X^3) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+354x^82+588x^83+2186x^84+1728x^85+1512x^86+2648x^87+2340x^88+1782x^89+2358x^90+1362x^91+906x^92+1270x^93+528x^94+60x^95+22x^96+6x^97+6x^98+14x^99+6x^101+6x^102

The gray image is a linear code over GF(3) with n=396, k=9 and d=246.
This code was found by Heurico 1.16 in 0.542 seconds.