The generator matrix

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

generates a code of length 34 over Z3[X]/(X^3) who´s minimum homogenous weight is 63.

Homogenous weight enumerator: w(x)=1x^0+408x^63+534x^64+646x^66+1644x^67+1072x^69+1620x^70+516x^72+60x^73+20x^75+30x^76+8x^78+2x^90

The gray image is a linear code over GF(3) with n=306, k=8 and d=189.
This code was found by Heurico 1.16 in 0.0683 seconds.