The generator matrix

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

generates a code of length 41 over Z3[X]/(X^3) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+34x^69+66x^70+66x^71+92x^72+144x^73+252x^74+102x^75+456x^76+384x^77+102x^78+1446x^79+3462x^80+86x^81+2766x^82+6564x^83+82x^84+1926x^85+576x^86+66x^87+378x^88+306x^89+52x^90+60x^91+42x^92+34x^93+48x^94+12x^95+26x^96+26x^99+16x^102+6x^105+4x^108

The gray image is a linear code over GF(3) with n=369, k=9 and d=207.
This code was found by Heurico 1.16 in 1.27 seconds.