The generator matrix

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

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+96x^82+294x^83+486x^84+684x^85+1956x^86+2392x^87+1968x^88+5298x^89+5882x^90+4422x^91+8958x^92+7940x^93+4386x^94+6606x^95+4012x^96+1230x^97+1560x^98+268x^99+216x^100+90x^101+106x^102+96x^103+24x^104+36x^105+24x^106+14x^108+4x^114

The gray image is a linear code over GF(3) with n=414, k=10 and d=246.
This code was found by Heurico 1.16 in 6.62 seconds.