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

generates a code of length 43 over Z3[X]/(X^3) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+366x^84+234x^87+112x^90+12x^93+4x^99

The gray image is a linear code over GF(3) with n=387, k=6 and d=252.
This code was found by Heurico 1.16 in 0.0821 seconds.