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

generates a code of length 71 over Z3[X]/(X^3) who´s minimum homogenous weight is 134.

Homogenous weight enumerator: w(x)=1x^0+174x^134+168x^135+276x^137+288x^138+1284x^140+780x^141+2250x^143+754x^144+156x^146+82x^147+48x^149+42x^150+114x^152+40x^153+54x^155+24x^156+18x^158+6x^159+2x^201

The gray image is a linear code over GF(3) with n=639, k=8 and d=402.
This code was found by Heurico 1.16 in 18 seconds.