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

generates a code of length 39 over Z3[X]/(X^3) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+234x^78+2x^81+6x^90

The gray image is a linear code over GF(3) with n=351, k=5 and d=234.
This code was found by Heurico 1.16 in 0.0128 seconds.