The generator matrix

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

generates a code of length 90 over Z3[X]/(X^2) who´s minimum homogenous weight is 177.

Homogenous weight enumerator: w(x)=1x^0+220x^177+396x^180+102x^186+6x^198+2x^204+2x^216

The gray image is a linear code over GF(3) with n=270, k=6 and d=177.
This code was found by Heurico 1.16 in 0.522 seconds.