The generator matrix

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

generates a code of length 96 over Z3[X]/(X^2) who´s minimum homogenous weight is 181.

Homogenous weight enumerator: w(x)=1x^0+186x^181+252x^182+92x^183+492x^184+552x^185+154x^186+444x^187+534x^188+102x^189+420x^190+432x^191+114x^192+450x^193+342x^194+86x^195+282x^196+234x^197+68x^198+204x^199+162x^200+40x^201+192x^202+180x^203+24x^204+84x^205+108x^206+12x^207+72x^208+66x^209+18x^210+54x^211+24x^212+6x^213+18x^214+24x^215+6x^216+18x^217+6x^218+6x^219

The gray image is a linear code over GF(3) with n=288, k=8 and d=181.
This code was found by Heurico 1.16 in 0.99 seconds.