The generator matrix

 1  0  1  1  1  1  1 2X^2+X  1 2X  1  1  1  1  0  1 2X^2+X  1  1  1  1 2X  1  1 2X^2+X  1 2X^2+X  1  1  1  1  1 2X^2+X X^2+X  1  1  1  1  1  0  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 2X^2+2X+1  1  0  1 2X^2+X 2X^2+X+2 X+1 2X  1 2X^2+1 2X+2  1 2X^2+X  1 X+1 2X^2+X 2X^2+X+2  0 2X+2  1  1 2X^2+1  0 2X 2X X^2+2X  1  0
 0  0 2X^2  0  0  0 2X^2 2X^2 X^2 2X^2 2X^2  0 X^2 2X^2 2X^2 2X^2 X^2 2X^2 2X^2  0 2X^2 2X^2 2X^2 2X^2 X^2  0  0  0  0  0 2X^2 2X^2 2X^2 2X^2 2X^2 X^2  0 2X^2 X^2 2X^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 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 2X^2  0  0 2X^2 2X^2 X^2  0 2X^2 2X^2 2X^2  0  0 X^2 X^2  0
 0  0  0  0 2X^2  0 X^2 2X^2 2X^2 2X^2 2X^2 2X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2 2X^2  0  0  0  0 2X^2 2X^2 2X^2  0  0  0 2X^2 2X^2 2X^2  0 X^2 2X^2 2X^2 2X^2  0  0
 0  0  0  0  0 X^2  0 2X^2 2X^2 X^2  0 X^2 X^2 2X^2 X^2 2X^2 2X^2 X^2  0 2X^2 2X^2  0 2X^2  0 X^2  0 2X^2  0 2X^2 2X^2 X^2 X^2  0 X^2  0 X^2 X^2 2X^2  0 X^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+58x^69+338x^72+108x^73+54x^74+1244x^75+1080x^76+432x^77+3870x^78+5940x^79+1296x^80+9708x^81+11070x^82+1728x^83+10222x^84+7668x^85+864x^86+2422x^87+378x^88+396x^90+94x^93+30x^96+22x^99+14x^102+10x^105+2x^108

The gray image is a linear code over GF(3) with n=369, k=10 and d=207.
This code was found by Heurico 1.16 in 5.46 seconds.