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

generates a code of length 88 over Z3[X]/(X^3) who´s minimum homogenous weight is 172.

Homogenous weight enumerator: w(x)=1x^0+36x^172+90x^173+28x^174+144x^175+1602x^176+48x^177+144x^178+90x^179+2x^180+2x^264

The gray image is a linear code over GF(3) with n=792, k=7 and d=516.
This code was found by Heurico 1.16 in 0.318 seconds.