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

generates a code of length 48 over Z3[X]/(X^3) who´s minimum homogenous weight is 90.

Homogenous weight enumerator: w(x)=1x^0+68x^90+254x^93+486x^94+168x^96+972x^97+104x^99+112x^102+18x^105+2x^117+2x^135

The gray image is a linear code over GF(3) with n=432, k=7 and d=270.
This code was found by Heurico 1.16 in 0.0584 seconds.