The generator matrix

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

generates a code of length 68 over Z3[X]/(X^3) who´s minimum homogenous weight is 128.

Homogenous weight enumerator: w(x)=1x^0+624x^128+1480x^129+2898x^130+3108x^131+3614x^132+4896x^133+4734x^134+5284x^135+6714x^136+4470x^137+4714x^138+5310x^139+3546x^140+2836x^141+2232x^142+1332x^143+710x^144+306x^145+102x^146+34x^147+24x^149+28x^150+36x^152+8x^153+6x^155+2x^159

The gray image is a linear code over GF(3) with n=612, k=10 and d=384.
This code was found by Heurico 1.16 in 55.9 seconds.