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

generates a code of length 90 over Z3[X]/(X^3) who´s minimum homogenous weight is 173.

Homogenous weight enumerator: w(x)=1x^0+402x^173+236x^174+108x^175+426x^176+398x^177+432x^178+918x^179+1026x^180+756x^181+708x^182+366x^183+162x^184+198x^185+38x^186+84x^188+62x^189+102x^191+42x^192+42x^194+14x^195+24x^197+12x^200+2x^210+2x^246

The gray image is a linear code over GF(3) with n=810, k=8 and d=519.
This code was found by Heurico 1.16 in 47.8 seconds.