The generator matrix

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

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+526x^126+342x^127+432x^128+2140x^129+1278x^130+2142x^131+4108x^132+3816x^133+4662x^134+6146x^135+6048x^136+6264x^137+6622x^138+4716x^139+3582x^140+3120x^141+1206x^142+414x^143+782x^144+90x^145+354x^147+168x^150+76x^153+8x^156+2x^159+2x^162+2x^165

The gray image is a linear code over GF(3) with n=612, k=10 and d=378.
This code was found by Heurico 1.16 in 10.2 seconds.