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

generates a code of length 49 over Z3[X]/(X^3) who´s minimum homogenous weight is 90.

Homogenous weight enumerator: w(x)=1x^0+164x^90+478x^93+888x^96+2916x^98+1556x^99+214x^102+174x^105+118x^108+46x^111+4x^117+2x^144

The gray image is a linear code over GF(3) with n=441, k=8 and d=270.
This code was found by Heurico 1.16 in 0.226 seconds.