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

generates a code of length 96 over Z3[X]/(X^3) who´s minimum homogenous weight is 180.

Homogenous weight enumerator: w(x)=1x^0+110x^180+18x^181+92x^183+108x^184+280x^186+210x^187+1076x^189+282x^190+2004x^192+408x^193+1342x^195+276x^196+44x^198+132x^199+28x^201+24x^202+32x^204+16x^207+14x^210+14x^213+20x^216+10x^219+2x^222+12x^228+2x^231+2x^234+2x^258

The gray image is a linear code over GF(3) with n=864, k=8 and d=540.
This code was found by Heurico 1.16 in 4.47 seconds.