The generator matrix

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

generates a code of length 39 over Z3[X]/(X^3) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+44x^66+168x^68+274x^69+108x^70+642x^71+1600x^72+864x^73+2394x^74+7096x^75+2592x^76+6288x^77+13650x^78+3456x^79+6384x^80+9348x^81+1728x^82+1278x^83+606x^84+294x^86+92x^87+48x^89+34x^90+28x^93+22x^96+6x^99+2x^102+2x^105

The gray image is a linear code over GF(3) with n=351, k=10 and d=198.
This code was found by Heurico 1.16 in 5.21 seconds.