The generator matrix

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

generates a code of length 41 over Z3[X]/(X^3) who´s minimum homogenous weight is 73.

Homogenous weight enumerator: w(x)=1x^0+510x^73+1212x^74+2022x^75+4524x^76+5466x^77+9192x^78+13896x^79+14190x^80+20674x^81+25092x^82+20952x^83+23218x^84+17976x^85+9078x^86+4746x^87+2952x^88+984x^89+118x^90+120x^91+102x^92+44x^93+36x^94+18x^95+6x^96+18x^97

The gray image is a linear code over GF(3) with n=369, k=11 and d=219.
This code was found by Heurico 1.16 in 37.9 seconds.