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

generates a code of length 68 over Z3[X]/(X^3) who´s minimum homogenous weight is 127.

Homogenous weight enumerator: w(x)=1x^0+138x^127+66x^129+318x^130+310x^132+276x^133+972x^134+830x^135+162x^136+1944x^137+856x^138+210x^139+84x^141+150x^142+20x^144+72x^145+12x^147+66x^148+60x^151+2x^153+6x^154+2x^159+2x^165+2x^189

The gray image is a linear code over GF(3) with n=612, k=8 and d=381.
This code was found by Heurico 1.16 in 0.833 seconds.