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

generates a code of length 43 over Z3[X]/(X^3) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+186x^82+300x^83+102x^84+408x^85+438x^86+120x^87+324x^88+186x^89+2x^90+6x^91+30x^92+16x^93+30x^94+18x^95+6x^97+12x^100+2x^111

The gray image is a linear code over GF(3) with n=387, k=7 and d=246.
This code was found by Heurico 1.16 in 0.0863 seconds.