The generator matrix

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

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+88x^180+216x^181+492x^182+772x^183+1176x^184+2538x^185+1834x^186+2634x^187+4182x^188+3382x^189+3924x^190+6114x^191+4226x^192+4494x^193+5868x^194+4220x^195+3372x^196+4122x^197+1660x^198+1170x^199+1188x^200+352x^201+246x^202+168x^203+92x^204+108x^205+60x^206+88x^207+96x^208+36x^209+30x^210+42x^211+12x^212+6x^213+6x^214+6x^215+8x^216+12x^217+4x^222+2x^225+2x^237

The gray image is a linear code over GF(3) with n=864, k=10 and d=540.
This code was found by Heurico 1.16 in 16.8 seconds.