The generator matrix

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

generates a code of length 39 over Z3[X]/(X^3) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+216x^69+216x^70+726x^71+1328x^72+1722x^73+3162x^74+3602x^75+5094x^76+7236x^77+9128x^78+8178x^79+8172x^80+5152x^81+2454x^82+1446x^83+486x^84+234x^85+108x^86+220x^87+66x^88+48x^89+32x^90+18x^91+4x^93

The gray image is a linear code over GF(3) with n=351, k=10 and d=207.
This code was found by Heurico 1.16 in 5.15 seconds.