The generator matrix

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

generates a code of length 41 over Z3[X]/(X^3) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+82x^72+162x^73+168x^74+324x^75+558x^76+396x^77+724x^78+1572x^79+1260x^80+1634x^81+5466x^82+1764x^83+1764x^84+1926x^85+582x^86+262x^87+354x^88+108x^89+234x^90+132x^91+84x^92+54x^93+36x^94+12x^95+16x^96+2x^99+6x^105

The gray image is a linear code over GF(3) with n=369, k=9 and d=216.
This code was found by Heurico 1.16 in 1.16 seconds.