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 X X 0 1 1 X X X^2 1 X X 2X^2 1 1 1 1 1 1 1
0 X 2X X^2 2X^2+X X^2+2X 2X^2 X^2+X 2X^2+2X 0 2X^2+X 2X X^2 X^2+X X^2+2X 2X^2 X 2X^2+2X 0 2X^2+X 2X X^2 X^2+X X^2+2X 2X^2+X 2X X 2X^2 X X^2+X X^2+2X X 2X^2+2X X 2X^2+2X X 0 X^2 2X^2 0 X^2 2X^2+X X^2+X
generates a code of length 43 over Z3[X]/(X^3) who´s minimum homogenous weight is 85.
Homogenous weight enumerator: w(x)=1x^0+24x^85+198x^86+2x^87+12x^88+2x^96+4x^102
The gray image is a linear code over GF(3) with n=387, k=5 and d=255.
This code was found by Heurico 1.16 in 0.0182 seconds.