The generator matrix 1 0 0 0 1 1 1 1 1 2X 1 1 1 1 1 1 1 2X 1 0 1 X 1 2X 1 2X 1 1 1 1 2X 1 1 1 1 1 2X 1 1 1 0 1 1 1 0 2X X 0 1 0 1 1 X 1 1 1 1 0 X 1 1 0 1 2X 1 1 1 1 1 1 1 1 1 1 1 1 2X 1 1 1 1 1 1 1 1 1 1 X 1 1 1 1 1 X 1 X 0 1 0 0 0 0 2X+1 2X+1 X+1 1 2 X+2 2X 2X+2 1 X+2 X+2 1 2X 1 2X+1 0 X+1 X 1 1 X+1 2X+2 0 X+2 1 2 2X X+2 X X 1 2 1 1 1 X+2 2X 1 1 X 1 1 2 1 2X+1 2 0 2 1 X X 1 1 2X+1 X+1 1 X+1 1 X+1 X+1 X+2 2X+2 0 2X+1 0 2X 2 1 X+2 2X+1 0 2 X+1 2X X+2 2 X 2X X X+1 2X X 2X X 2X+1 X+2 2 0 X+1 1 0 0 1 0 0 X X 2X 0 0 2X 2X 2X+1 1 1 2X+2 2 X+1 X+1 X+2 X+1 1 2X+2 1 2X+2 1 2X+2 X+2 X+2 1 X+1 X+1 X+2 0 2X+2 2X+1 0 2X 1 2 0 X+1 X X 2 1 X+1 X+2 2X+1 2X+1 0 X 2X X+2 2 2 0 2 2X 2X+1 X 2X+2 0 2 2 1 2X+1 X+2 2X+2 X+1 X+1 2X 2X+2 X+2 0 2X 0 X+2 X X+1 1 2X 2X X+1 2X+2 2 2X 1 X+2 X X+1 0 1 1 2X+2 X+2 0 0 0 1 1 2X+2 2 1 0 X+2 0 2X+1 X 2X X X+1 0 X+1 2X+1 2X+2 X+2 X+2 1 X+1 2X+2 2 X 2 X+1 1 2X 2 2 X+2 X 0 X+1 2X 2X+1 2 X 0 2 X+1 X 2 1 2X+2 1 2X+1 2 0 1 2X X+2 X+1 X 1 2X+2 1 X+1 X+2 X+2 2X X 2X+2 0 1 X+2 X+2 1 X X+2 X+1 2 X 1 2 2 X 2 X+2 2X+1 2X+2 X+2 2X 0 X+1 2X X+1 1 2X+2 2 2X 2X+1 X 0 0 0 0 2X 2X 2X 2X 2X 0 2X 2X 2X 2X 2X 2X 2X 0 2X 0 2X 0 2X 0 2X 2X X 0 X 0 2X 0 X X 0 X X 0 X X X X 0 X 2X X 2X X X X X X 2X X 0 0 X 0 X 0 0 2X 0 X 2X 0 0 X 0 X X 2X X 2X 0 X X 2X X 0 2X 2X X 0 2X 0 X 2X X 2X 2X 0 X X 0 0 generates a code of length 96 over Z3[X]/(X^2) who´s minimum homogenous weight is 178. Homogenous weight enumerator: w(x)=1x^0+312x^178+450x^179+170x^180+756x^181+978x^182+216x^183+1050x^184+1002x^185+310x^186+1074x^187+1230x^188+290x^189+1182x^190+1086x^191+310x^192+1176x^193+1182x^194+286x^195+930x^196+888x^197+218x^198+864x^199+762x^200+156x^201+630x^202+576x^203+112x^204+426x^205+348x^206+66x^207+234x^208+156x^209+36x^210+78x^211+66x^212+12x^213+30x^214+18x^215+2x^216+6x^217+6x^218+2x^219 The gray image is a linear code over GF(3) with n=288, k=9 and d=178. This code was found by Heurico 1.16 in 49.3 seconds.