The generator matrix

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

generates a code of length 41 over Z3[X]/(X^3) who´s minimum homogenous weight is 75.

Homogenous weight enumerator: w(x)=1x^0+1086x^75+1026x^76+1818x^77+4206x^78+4446x^79+5400x^80+7808x^81+6264x^82+7236x^83+7864x^84+5022x^85+2880x^86+2826x^87+738x^88+162x^89+174x^90+82x^93+6x^96+4x^102

The gray image is a linear code over GF(3) with n=369, k=10 and d=225.
This code was found by Heurico 1.16 in 5.57 seconds.