The generator matrix

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

generates a code of length 68 over Z3[X]/(X^3) who´s minimum homogenous weight is 130.

Homogenous weight enumerator: w(x)=1x^0+804x^130+1362x^131+1780x^132+2202x^133+1794x^134+1604x^135+1926x^136+1806x^137+1088x^138+1410x^139+1128x^140+768x^141+936x^142+492x^143+334x^144+168x^145+54x^146+10x^147+6x^148+2x^150+6x^152+2x^153

The gray image is a linear code over GF(3) with n=612, k=9 and d=390.
This code was found by Heurico 1.16 in 0.93 seconds.