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

generates a code of length 93 over Z3[X]/(X^3) who´s minimum homogenous weight is 178.

Homogenous weight enumerator: w(x)=1x^0+198x^178+36x^179+230x^180+306x^181+666x^182+136x^183+360x^184+1674x^185+64x^186+222x^187+1800x^188+152x^189+78x^190+198x^191+62x^192+96x^193+8x^195+84x^196+72x^198+48x^199+30x^202+36x^205+2x^225+2x^252

The gray image is a linear code over GF(3) with n=837, k=8 and d=534.
This code was found by Heurico 1.16 in 0.797 seconds.