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

generates a code of length 90 over Z3[X]/(X^3) who´s minimum homogenous weight is 162.

Homogenous weight enumerator: w(x)=1x^0+120x^162+198x^165+6x^166+262x^168+24x^169+182x^171+144x^172+182x^174+600x^175+188x^177+1140x^178+13282x^180+1260x^181+136x^183+960x^184+134x^186+240x^187+136x^189+96x^192+118x^195+84x^198+70x^201+38x^204+40x^207+20x^210+14x^213+6x^216+2x^249

The gray image is a linear code over GF(3) with n=810, k=9 and d=486.
This code was found by Heurico 1.16 in 12.6 seconds.