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

generates a code of length 90 over Z3[X]/(X^3) who´s minimum homogenous weight is 168.

Homogenous weight enumerator: w(x)=1x^0+122x^168+12x^169+112x^171+144x^172+180x^175+204x^177+1686x^178+58x^180+3384x^181+306x^184+92x^186+84x^187+42x^189+36x^190+28x^195+12x^198+30x^204+8x^207+8x^213+8x^216+2x^225+2x^240

The gray image is a linear code over GF(3) with n=810, k=8 and d=504.
This code was found by Heurico 1.16 in 0.946 seconds.