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

generates a code of length 43 over Z3[X]/(X^3) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+126x^81+438x^84+972x^86+474x^87+76x^90+84x^93+12x^96+2x^99+2x^126

The gray image is a linear code over GF(3) with n=387, k=7 and d=243.
This code was found by Heurico 1.16 in 0.0436 seconds.