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

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+416x^126+1128x^129+108x^130+54x^131+1590x^132+486x^133+1458x^134+3026x^135+3078x^136+2754x^137+2868x^138+702x^139+108x^140+792x^141+512x^144+336x^147+174x^150+84x^153+6x^156+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 2.15 seconds.