The generator matrix

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

generates a code of length 73 over Z3[X]/(X^3) who´s minimum homogenous weight is 138.

Homogenous weight enumerator: w(x)=1x^0+268x^138+324x^139+702x^140+1436x^141+1014x^142+1860x^143+1682x^144+1602x^145+1860x^146+2130x^147+1548x^148+1656x^149+1482x^150+714x^151+654x^152+366x^153+120x^154+30x^155+90x^156+18x^157+18x^158+30x^159+6x^161+20x^162+6x^163+18x^164+14x^165+4x^168+10x^171

The gray image is a linear code over GF(3) with n=657, k=9 and d=414.
This code was found by Heurico 1.16 in 1.52 seconds.