The generator matrix

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

generates a code of length 69 over Z3[X]/(X^3) who´s minimum homogenous weight is 135.

Homogenous weight enumerator: w(x)=1x^0+276x^135+504x^136+774x^138+342x^139+30x^141+72x^142+126x^144+54x^145+6x^150+2x^162

The gray image is a linear code over GF(3) with n=621, k=7 and d=405.
This code was found by Heurico 1.16 in 0.126 seconds.