The generator matrix

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

generates a code of length 44 over Z3[X]/(X^3) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+428x^81+126x^82+1026x^83+1732x^84+684x^85+1908x^86+3112x^87+1188x^88+2862x^89+3040x^90+900x^91+1458x^92+896x^93+18x^94+36x^95+164x^96+82x^99+18x^102+2x^108+2x^117

The gray image is a linear code over GF(3) with n=396, k=9 and d=243.
This code was found by Heurico 1.16 in 0.725 seconds.