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

generates a code of length 46 over Z3[X]/(X^3) who´s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+174x^88+282x^89+356x^90+120x^91+264x^92+496x^93+126x^94+252x^95+12x^96+18x^97+6x^98+12x^99+24x^100+6x^101+12x^102+18x^103+6x^106+2x^120

The gray image is a linear code over GF(3) with n=414, k=7 and d=264.
This code was found by Heurico 1.16 in 37.9 seconds.