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

generates a code of length 49 over Z3[X]/(X^3) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+66x^81+168x^84+218x^87+212x^90+162x^92+188x^93+972x^95+244x^96+15066x^98+218x^99+1296x^101+188x^102+210x^105+168x^108+132x^111+76x^114+62x^117+24x^120+8x^123+2x^126+2x^138

The gray image is a linear code over GF(3) with n=441, k=9 and d=243.
This code was found by Heurico 1.16 in 2.34 seconds.