The generator matrix

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

generates a code of length 44 over Z3[X]/(X^3) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+72x^86+84x^87+378x^88+144x^89+44x^90+2x^96+4x^105

The gray image is a linear code over GF(3) with n=396, k=6 and d=258.
This code was found by Heurico 1.16 in 0.0142 seconds.