The generator matrix

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

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+84x^73+54x^74+270x^75+546x^76+432x^77+1056x^78+1578x^79+1296x^80+3072x^81+2700x^82+1728x^83+3070x^84+1950x^85+864x^86+502x^87+330x^88+24x^90+96x^91+4x^93+6x^94+4x^96+6x^99+4x^102+4x^105+2x^108

The gray image is a linear code over GF(3) with n=369, k=9 and d=219.
This code was found by Heurico 1.16 in 0.72 seconds.