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

generates a code of length 84 over Z3[X]/(X^3) who´s minimum homogenous weight is 165.

Homogenous weight enumerator: w(x)=1x^0+144x^165+72x^166+272x^168+84x^169+118x^171+22x^174+4x^177+6x^178+4x^180+2x^183

The gray image is a linear code over GF(3) with n=756, k=6 and d=495.
This code was found by Heurico 1.16 in 0.318 seconds.