The generator matrix

 1  0  0  1  1  1  1  1  1  1 2X^2  1 2X^2+X  1  1  1 X^2+X  1  1  1 X^2  1 2X^2+X  1 2X^2  1  X 2X^2+2X  1  1 2X^2+X  1  1  1  1  1  1  1 X^2+X  1  1  1 X^2+2X  1  1  1  1  1 X^2+2X 2X^2+X X^2+2X  1  0  0  1 2X  X  1  1  1  1  1  1  1  1  X  1  1  1  1  0
 0  1  0  0 X^2 2X^2+2X+1 2X+1 X+2 2X^2+X+1 X^2+X+2  1  2  1 2X^2+X 2X^2+2X+2 X^2+2X+1  1 2X+2 X^2+2X+1 2X^2+1  1 2X^2+X+2 2X^2+2X 2X^2  1 2X^2  1  1 X^2+2 2X  1 2X^2+1 2X+2 X^2+X+1  2 2X^2+X 2X^2+2X X^2+1 X^2+X  X 2X X^2+1  1 X+1 X^2+X 2X^2+2X+1  1 X^2+2X+2  1  1 2X^2 X^2+X  0  1 X+1  1  1 2X^2+X+1 X^2+2X 2X^2+X+1 X+1 X^2+2 X^2+2X  1 X+2 2X^2+2X  1 2X^2+2X X^2+2X+2 2X^2+X+1  1
 0  0  1 2X^2+2X+1 2X^2+2 X^2+2 2X+1 X^2+X 2X^2+X X^2+X+2 2X^2+1 X+1 2X^2+2X+2 2X^2 2X^2+2X+1 X^2+2X 2X^2+1 2X X^2+2X+2 2X^2+X+1 2X^2+X+2 2X^2+2  1 X+1 2X^2+2X X+2 X+2 X^2 2X+1 2X^2+1 2X^2+2X+1 X^2+2X+1 X^2 2X^2 2X^2+2 2X^2+X X^2+X+2 2X^2+X  1 2X^2+X+1 2X^2 X+2 X^2+2X+1 X^2+2 X+1  1 2X^2+2X 2X^2+X+1 X^2+X+1 X^2+X  1 X^2+X  1 X^2+X 2X^2+X+2 X^2+2X X^2+X+2 2X^2+2X  X 2X^2+X+2 2X^2+2X+2 X^2+2X+1 X^2+2X+2 X^2 X^2+2X+2  1 2X X+1 2X^2+2X+1 X+2 2X^2+X+2
 0  0  0 2X^2 2X^2 2X^2 2X^2 2X^2 2X^2 2X^2  0 2X^2  0 2X^2 X^2  0 X^2  0 X^2 X^2 X^2  0 2X^2  0 X^2 X^2 2X^2 2X^2  0 X^2 2X^2  0 X^2 X^2 X^2 X^2  0 2X^2 X^2 2X^2 2X^2  0 X^2 X^2 X^2  0 X^2 2X^2 2X^2 2X^2  0  0 X^2 X^2 2X^2  0 X^2 X^2 X^2 X^2 2X^2 X^2  0  0  0  0  0  0  0  0 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+846x^134+2190x^135+1818x^136+2886x^137+5192x^138+3816x^139+3684x^140+7350x^141+5004x^142+4008x^143+7024x^144+3582x^145+3030x^146+4216x^147+1584x^148+1260x^149+924x^150+234x^151+246x^152+22x^153+42x^155+40x^156+24x^158+6x^159+12x^161+6x^162+2x^165

The gray image is a linear code over GF(3) with n=639, k=10 and d=402.
This code was found by Heurico 1.16 in 8.67 seconds.