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

generates a code of length 46 over Z3[X]/(X^3) who�s minimum homogenous weight is 87.

Homogenous weight enumerator: w(x)=1x^0+72x^87+120x^88+108x^89+440x^90+258x^91+772x^93+216x^94+60x^96+42x^97+54x^98+22x^99+12x^100+6x^102+2x^111+2x^126

The gray image is a linear code over GF(3) with n=414, k=7 and d=261.
This code was found by Heurico 1.16 in 0.0518 seconds.