The generator matrix

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

generates a code of length 38 over Z3[X]/(X^3) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+86x^66+66x^67+120x^68+434x^69+360x^70+300x^71+1186x^72+906x^73+1746x^74+2698x^75+3078x^76+3174x^77+2716x^78+1140x^79+306x^80+536x^81+174x^82+108x^83+268x^84+96x^85+72x^86+70x^87+12x^88+6x^89+12x^90+8x^93+2x^96+2x^99

The gray image is a linear code over GF(3) with n=342, k=9 and d=198.
This code was found by Heurico 1.16 in 1.05 seconds.