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

generates a code of length 71 over Z3[X]/(X^3) who´s minimum homogenous weight is 135.

Homogenous weight enumerator: w(x)=1x^0+410x^135+18x^136+742x^138+108x^139+324x^140+1540x^141+702x^142+648x^143+1388x^144+144x^145+224x^147+92x^150+110x^153+96x^156+6x^159+6x^162+2x^198

The gray image is a linear code over GF(3) with n=639, k=8 and d=405.
This code was found by Heurico 1.16 in 0.935 seconds.