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

generates a code of length 97 over Z3[X]/(X^3) who´s minimum homogenous weight is 180.

Homogenous weight enumerator: w(x)=1x^0+130x^180+6x^181+96x^182+330x^183+114x^184+168x^185+486x^186+552x^187+204x^188+988x^189+1596x^190+192x^191+1720x^192+3210x^193+210x^194+2150x^195+3198x^196+144x^197+1292x^198+1362x^199+162x^200+330x^201+132x^202+162x^203+240x^204+30x^205+78x^206+172x^207+6x^208+36x^209+92x^210+24x^213+6x^215+30x^216+10x^219+10x^222+6x^225+2x^228+2x^231+2x^240+2x^249

The gray image is a linear code over GF(3) with n=873, k=9 and d=540.
This code was found by Heurico 1.16 in 4.08 seconds.