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

generates a code of length 90 over Z3[X]/(X^2) who´s minimum homogenous weight is 156.

Homogenous weight enumerator: w(x)=1x^0+126x^156+292x^159+362x^162+6x^164+424x^165+114x^167+434x^168+402x^170+478x^171+1122x^173+488x^174+2094x^176+488x^177+3192x^179+476x^180+3084x^182+496x^183+2166x^185+536x^186+780x^188+484x^189+162x^191+366x^192+320x^195+284x^198+160x^201+160x^204+94x^207+42x^210+36x^213+8x^216+2x^219+2x^222+2x^237

The gray image is a linear code over GF(3) with n=270, k=9 and d=156.
This code was found by Heurico 1.16 in 18.1 seconds.