The generator matrix

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

generates a code of length 71 over Z3[X]/(X^3) who´s minimum homogenous weight is 137.

Homogenous weight enumerator: w(x)=1x^0+480x^137+586x^138+612x^139+1194x^140+534x^141+504x^142+606x^143+334x^144+396x^145+522x^146+344x^147+108x^148+258x^149+48x^150+6x^152+2x^153+10x^156+6x^158+2x^162+6x^164+2x^165

The gray image is a linear code over GF(3) with n=639, k=8 and d=411.
This code was found by Heurico 1.16 in 0.251 seconds.