The generator matrix

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

generates a code of length 97 over Z3[X]/(X^2) who´s minimum homogenous weight is 176.

Homogenous weight enumerator: w(x)=1x^0+138x^176+224x^177+450x^178+798x^179+992x^180+888x^181+1410x^182+1464x^183+1410x^184+1932x^185+1876x^186+1890x^187+2556x^188+2228x^189+2202x^190+2610x^191+2588x^192+2346x^193+2970x^194+2400x^195+2442x^196+2958x^197+2664x^198+1956x^199+2346x^200+2312x^201+1656x^202+1884x^203+1502x^204+1278x^205+1212x^206+880x^207+618x^208+624x^209+348x^210+222x^211+342x^212+154x^213+114x^214+72x^215+46x^216+24x^217+12x^218+2x^219+6x^221+2x^225

The gray image is a linear code over GF(3) with n=291, k=10 and d=176.
This code was found by Heurico 1.16 in 82.5 seconds.