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

generates a code of length 97 over Z3[X]/(X^3) who´s minimum homogenous weight is 180.

Homogenous weight enumerator: w(x)=1x^0+42x^180+114x^183+174x^186+272x^189+464x^192+4374x^194+490x^195+352x^198+126x^201+34x^204+26x^207+22x^210+20x^213+12x^216+4x^219+16x^222+4x^225+6x^228+4x^231+2x^237+2x^270

The gray image is a linear code over GF(3) with n=873, k=8 and d=540.
This code was found by Heurico 1.16 in 0.998 seconds.