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

generates a code of length 96 over Z3[X]/(X^3) who´s minimum homogenous weight is 183.

Homogenous weight enumerator: w(x)=1x^0+90x^183+72x^184+78x^185+260x^186+168x^187+678x^188+318x^189+366x^190+1458x^191+192x^192+714x^193+1014x^194+176x^195+510x^196+66x^197+60x^198+42x^199+24x^201+12x^202+42x^203+32x^204+24x^205+66x^206+60x^207+24x^208+12x^211+2x^270

The gray image is a linear code over GF(3) with n=864, k=8 and d=549.
This code was found by Heurico 1.16 in 1.27 seconds.