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

generates a code of length 88 over Z3[X]/(X^3) who´s minimum homogenous weight is 174.

Homogenous weight enumerator: w(x)=1x^0+30x^174+648x^176+36x^177+6x^180+2x^183+2x^189+4x^210

The gray image is a linear code over GF(3) with n=792, k=6 and d=522.
This code was found by Heurico 1.16 in 0.382 seconds.