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

generates a code of length 68 over Z3[X]/(X^3) who´s minimum homogenous weight is 126.

Homogenous weight enumerator: w(x)=1x^0+498x^126+896x^129+54x^130+2082x^132+324x^133+972x^134+4344x^135+2106x^136+1944x^137+4180x^138+432x^139+710x^141+486x^144+412x^147+176x^150+42x^153+20x^156+2x^159+2x^189

The gray image is a linear code over GF(3) with n=612, k=9 and d=378.
This code was found by Heurico 1.16 in 2.21 seconds.