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

generates a code of length 96 over Z3[X]/(X^3) who´s minimum homogenous weight is 177.

Homogenous weight enumerator: w(x)=1x^0+82x^177+6x^178+54x^179+178x^180+120x^181+150x^182+360x^183+192x^184+384x^185+484x^186+180x^187+1878x^188+552x^189+192x^190+5544x^191+614x^192+216x^193+5526x^194+440x^195+234x^196+720x^197+378x^198+156x^199+174x^200+234x^201+72x^202+84x^203+94x^204+66x^205+48x^206+74x^207+18x^208+18x^209+68x^210+6x^211+34x^213+22x^216+18x^219+8x^225+2x^228+2x^261

The gray image is a linear code over GF(3) with n=864, k=9 and d=531.
This code was found by Heurico 1.16 in 3.99 seconds.