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

generates a code of length 34 over Z3[X]/(X^3) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+246x^62+200x^63+108x^64+366x^65+1040x^66+432x^67+1320x^68+1672x^69+432x^70+234x^71+120x^72+174x^74+110x^75+84x^77+2x^78+6x^80+12x^81+2x^93

The gray image is a linear code over GF(3) with n=306, k=8 and d=186.
This code was found by Heurico 1.16 in 0.456 seconds.