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

generates a code of length 97 over Z3[X]/(X^3) who´s minimum homogenous weight is 186.

Homogenous weight enumerator: w(x)=1x^0+276x^186+524x^189+486x^190+444x^192+1944x^193+360x^195+1944x^196+178x^198+120x^201+54x^204+132x^207+84x^210+12x^213+2x^279

The gray image is a linear code over GF(3) with n=873, k=8 and d=558.
This code was found by Heurico 1.16 in 8.58 seconds.