The generator matrix

 1  0  1  1  1  1  1  0  1  1  1  0  1  1  1  0  1  X  1  1  0  1  1  1  0  1  1  1  1  0  1  1  1  1  1  1  1  1  0 2X  1  1  0  1  1  1  1  1  1  X 2X  X  1  1  1 2X  1  1  1  0  1  1 2X  1  1  1  1  X  1  0  1  1  1  1  1  1  1  1  1  X  X  1  0  0  1  X  0  X  1  1
 0  1  1  2  0  1  2  1  0 2X+1  2  1  0  2 2X+1  1 2X+1  1  0  2  1 2X+1  X  2  1  0 2X+1  2 2X+1  1  0 X+2 2X+1  2  X X+2  0 X+1  1  1 2X+1 2X+2  1  1  X 2X+2  X  X 2X+1  1  1  1 X+1 2X X+2  1 X+2  0  X  1 2X+1  X  1  1 2X+2 2X+1 2X+2  1  1  1 2X+1 2X+1  2  2  1  1 X+2  0  2  1  1 X+1  1  X  X  1  X  0 2X+2  0
 0  0 2X  0  0  0  0  0  0 2X  X  0  X  X 2X  X  0  X  X  X  X  0 2X 2X  0  X  X 2X  X  0  0 2X 2X 2X  0 2X 2X  X 2X  0 2X  X  X  0 2X 2X  0  0  0 2X  0  0  X 2X 2X  0 2X  X  X 2X  0  X 2X  0 2X 2X 2X  X  0 2X  0 2X  0  X 2X 2X  0  0 2X 2X  X 2X  X 2X  X 2X  X  0  X 2X
 0  0  0  X  0  0  0  0  0  0  0  0  0  0 2X 2X 2X 2X 2X  X  X 2X 2X  X  X  X  0  X  0  X  0 2X 2X 2X 2X 2X  0  0  0  0  X  0  X 2X  X  0  X  0 2X 2X 2X  X  X  0  X 2X  X  X  X  0 2X  X  X  0 2X 2X  0 2X  0  X  X  X 2X 2X  0  X  X  0 2X  X 2X 2X 2X  X 2X  X  0  0  X  0
 0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  0  X 2X 2X  X  X 2X  X  X 2X  X  X  X  X 2X 2X  X  0  0 2X  X 2X  X 2X 2X  0  X 2X 2X  X 2X 2X  0 2X  0 2X  0  X  0  0  0 2X 2X  X  X  0  0 2X  X  X 2X 2X  X  X 2X 2X  0 2X 2X 2X 2X  0  0  0  X 2X
 0  0  0  0  0 2X  0  0  0  0  0 2X  0  X  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X  X 2X 2X 2X  0 2X 2X 2X  0  0  X 2X  X  X  X  0 2X 2X 2X 2X 2X  X  0 2X  X  0 2X  0  X 2X  X  X  X  X  X  X 2X  X  X  0  0 2X 2X  0 2X  X 2X  0  0  X  0 2X 2X  0  X  X  X 2X 2X  X 2X  X  X 2X  X
 0  0  0  0  0  0  X  0 2X 2X  X  0  0 2X 2X 2X  X 2X  0  X  0  0  0  0 2X 2X  X  0 2X  0  X  X 2X  X  X  X  X  0  0  0 2X  0 2X  0  X 2X  X  X  X 2X 2X 2X  X 2X  0  0  0 2X  0 2X  X  X 2X  X  0  0  X  0 2X 2X 2X  0 2X  0 2X  X  X 2X  0 2X  0 2X 2X  X  X  0 2X  0 2X  0
 0  0  0  0  0  0  0  X  X 2X  0  X 2X  X  X  X  X 2X  0 2X  X 2X 2X 2X 2X 2X  0  0 2X  0  X 2X  0 2X  X 2X  0  X  X  0 2X  0  0 2X  0 2X 2X  X 2X  0  0  X  X  X  X  0  0  0 2X 2X  0  0  X  0  0 2X  0  X  X 2X  X 2X  0  0  X  0  0  0  X  X  0  0  X 2X 2X  0 2X  X 2X  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+24x^158+310x^159+300x^161+470x^162+618x^164+670x^165+1398x^167+1012x^168+2424x^170+1410x^171+3774x^173+1902x^174+5106x^176+2592x^177+6606x^179+2674x^180+6558x^182+2594x^183+5514x^185+2102x^186+3714x^188+1422x^189+2106x^191+940x^192+900x^194+618x^195+240x^197+342x^198+66x^200+192x^201+18x^203+138x^204+74x^207+52x^210+30x^213+6x^216+4x^219+2x^222

The gray image is a linear code over GF(3) with n=270, k=10 and d=156.
This code was found by Heurico 1.16 in 86.9 seconds.