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

generates a code of length 54 over Z3[X]/(X^3) who´s minimum homogenous weight is 90.

Homogenous weight enumerator: w(x)=1x^0+58x^90+154x^93+172x^96+306x^99+588x^102+1162x^105+14746x^108+1342x^111+588x^114+176x^117+144x^120+110x^123+68x^126+40x^129+20x^132+6x^135+2x^144

The gray image is a linear code over GF(3) with n=486, k=9 and d=270.
This code was found by Heurico 1.16 in 2.64 seconds.