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

generates a code of length 90 over Z3[X]/(X^3) who´s minimum homogenous weight is 171.

Homogenous weight enumerator: w(x)=1x^0+74x^171+84x^172+286x^174+108x^175+648x^176+310x^177+42x^178+1296x^179+78x^180+3000x^181+156x^183+36x^184+92x^186+42x^187+36x^189+30x^190+78x^192+18x^193+102x^195+24x^196+18x^199+2x^264

The gray image is a linear code over GF(3) with n=810, k=8 and d=513.
This code was found by Heurico 1.16 in 0.781 seconds.