The generator matrix

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

generates a code of length 96 over Z3[X]/(X^3) who´s minimum homogenous weight is 180.

Homogenous weight enumerator: w(x)=1x^0+312x^180+594x^181+1566x^182+3252x^183+4014x^184+5310x^185+8298x^186+7740x^187+9702x^188+12292x^189+12816x^190+13482x^191+14712x^192+14526x^193+14328x^194+13788x^195+11520x^196+8586x^197+7710x^198+4788x^199+3150x^200+2274x^201+792x^202+666x^203+336x^204+72x^205+72x^206+234x^207+132x^210+54x^213+16x^216+6x^219+6x^222

The gray image is a linear code over GF(3) with n=864, k=11 and d=540.
This code was found by Heurico 1.16 in 106 seconds.