The generator matrix

 1  0  1  1  1  1  1 2X^2  1  1 2X^2+X  1 2X^2+X  1  1  1 2X  1  1 2X  1  1  1  1  1  1  1  X  1  1  1  1  1 2X^2  X 2X^2+2X  1  1
 0  1  1  2 2X^2+2X+1 2X^2 2X^2+2  1 2X+1 2X^2+X+2  1 2X^2+2X  1 2X^2+X+2 X+1  0  1  1  X  1  2 2X^2+2X+1  0 X+1 2X^2+X+2  X 2X  1 2X^2+1  1  0  2  2  X  1  1 2X^2+X+2  0
 0  0 2X  0  0 2X^2+X 2X^2+X 2X^2+X  X 2X^2+2X 2X^2 2X^2+X 2X^2+2X X^2 2X 2X^2+2X 2X^2+2X X^2+X 2X^2+X 2X^2+2X X^2+2X 2X X^2+2X X^2  0 2X^2+X  0 X^2+X 2X^2 X^2+X 2X^2  0 2X^2+2X  X 2X^2  X 2X  0
 0  0  0 X^2  0 2X^2 X^2 X^2 X^2  0  0 2X^2  0 2X^2 X^2 X^2 2X^2 X^2  0 X^2 X^2 2X^2  0 X^2 2X^2  0 X^2  0 2X^2  0  0  0 2X^2 2X^2 2X^2 2X^2 2X^2 X^2
 0  0  0  0 2X^2  0  0 2X^2 2X^2 2X^2 X^2 X^2 2X^2 X^2  0 X^2 2X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0 2X^2 X^2 X^2  0 X^2 2X^2  0  0  0 2X^2 2X^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+102x^66+102x^67+252x^68+980x^69+1008x^70+1752x^71+2884x^72+3768x^73+5652x^74+7624x^75+8610x^76+7896x^77+7450x^78+4914x^79+3234x^80+1710x^81+480x^82+144x^83+262x^84+72x^85+24x^86+100x^87+16x^90+4x^93+2x^96+6x^99

The gray image is a linear code over GF(3) with n=342, k=10 and d=198.
This code was found by Heurico 1.16 in 4.97 seconds.