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

generates a code of length 46 over Z3[X]/(X^3) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+164x^81+90x^82+72x^83+272x^84+180x^85+342x^86+440x^87+702x^88+108x^89+3712x^90+2196x^91+234x^92+6780x^93+2232x^94+450x^95+542x^96+270x^97+216x^98+266x^99+144x^100+18x^101+108x^102+18x^103+18x^104+38x^105+34x^108+22x^111+6x^114+6x^117+2x^126

The gray image is a linear code over GF(3) with n=414, k=9 and d=243.
This code was found by Heurico 1.16 in 1.5 seconds.