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

generates a code of length 69 over Z3[X]/(X^3) who´s minimum homogenous weight is 139.

Homogenous weight enumerator: w(x)=1x^0+60x^139+6x^141+12x^142+2x^144

The gray image is a linear code over GF(3) with n=621, k=4 and d=417.
This code was found by Heurico 1.16 in 0.38 seconds.