The generator matrix

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

generates a code of length 46 over Z3[X]/(X^3) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+1098x^82+1764x^83+4836x^84+8520x^85+12060x^86+19958x^87+29256x^88+33762x^89+46942x^90+64404x^91+60822x^92+66892x^93+67320x^94+45012x^95+32596x^96+20574x^97+8592x^98+4786x^99+1668x^100+270x^101+152x^102+84x^103+42x^104+12x^105+12x^106+6x^109

The gray image is a linear code over GF(3) with n=414, k=12 and d=246.
This code was found by Heurico 1.16 in 347 seconds.