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

generates a code of length 39 over Z3[X]/(X^3) who´s minimum homogenous weight is 75.

Homogenous weight enumerator: w(x)=1x^0+72x^75+234x^76+84x^78+180x^79+80x^81+72x^82+6x^87

The gray image is a linear code over GF(3) with n=351, k=6 and d=225.
This code was found by Heurico 1.16 in 0.019 seconds.