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

generates a code of length 69 over Z3[X]/(X^3) who´s minimum homogenous weight is 129.

Homogenous weight enumerator: w(x)=1x^0+104x^129+66x^130+288x^132+126x^133+216x^134+192x^135+72x^136+864x^137+3104x^138+72x^139+864x^140+118x^141+60x^142+158x^144+24x^145+46x^147+24x^148+80x^150+30x^151+36x^153+12x^154+2x^156+2x^201

The gray image is a linear code over GF(3) with n=621, k=8 and d=387.
This code was found by Heurico 1.16 in 0.423 seconds.