The generator matrix

 1  0  1  1  1  1  1 2X^2+X  1  1  1 2X  1  1  1  1  1  1  0  1 2X^2+X  1  1 2X  1  1  1 X^2  1  1  1  1  1  1  1 2X X^2+2X X^2+X  1  1  1  1  0 2X^2+X  1 X^2+X
 0  1 2X^2+2X+1  2 2X^2+X X+1 2X^2+X+2  1 2X 2X+2 2X^2+1  1 X+1  0  2 2X^2+X 2X^2+X+2 2X  1 2X^2+2X+1  1 2X^2+1 2X+2  1 X^2 X^2+2X+1 X^2+2X+2  1 2X^2+1 X^2+1 X^2+X+1 2X X^2+2X  2 X^2+2  1  1  1  0 2X+2 2X^2+2X+1 X+1  1  1 2X^2+X+1  1
 0  0 2X^2  0 2X^2 X^2 X^2 X^2  0  0 X^2  0 X^2  0 X^2 2X^2 X^2 2X^2  0 2X^2 X^2 2X^2  0 X^2  0 2X^2  0  0 2X^2 X^2 X^2  0 2X^2  0 X^2  0 X^2 X^2 2X^2 X^2 X^2  0 X^2 2X^2 2X^2  0
 0  0  0 X^2 2X^2 2X^2 X^2  0 X^2 2X^2  0 2X^2 X^2 2X^2  0 X^2 2X^2  0 X^2 2X^2 X^2 X^2  0 2X^2 X^2 X^2 X^2 2X^2 2X^2 2X^2  0 2X^2 X^2  0 X^2  0 X^2 2X^2 2X^2 2X^2 X^2 2X^2  0 2X^2  0 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+640x^87+396x^88+1312x^90+648x^91+1688x^93+756x^94+906x^96+144x^97+60x^99+4x^102+4x^108+2x^132

The gray image is a linear code over GF(3) with n=414, k=8 and d=261.
This code was found by Heurico 1.16 in 4.43 seconds.