The generator matrix

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

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+394x^72+1314x^73+4512x^74+6390x^75+11988x^76+17988x^77+25766x^78+36990x^79+49800x^80+61454x^81+69744x^82+71580x^83+64362x^84+49014x^85+32616x^86+15540x^87+7704x^88+3240x^89+716x^90+114x^91+66x^92+66x^93+36x^94+12x^95+28x^96+6x^98

The gray image is a linear code over GF(3) with n=369, k=12 and d=216.
This code was found by Heurico 1.16 in 302 seconds.