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 1 0 2X 1 0 2X 1 1 1 1 1 1 X 1 1 1 1 1 1 X 1 1 1 1 1 2X 1 X X 1 1 1 0 1 1 1 1 X 1 1 2X 2X 0 0 1 X 0 1 1 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 0 1 1 X 1 X X 0 1 2 2 X 1 X+1 2X 2X X+1 X+2 X 0 1 2X+1 X+2 2 2 1 2X 1 X 2X 0 0 2X 2 2X X+1 2 1 X 2X+1 2X 1 X 1 1 0 1 2X+1 2X 0 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 X+1 X+1 1 2X+2 2X+1 1 2 2X+2 2X+1 1 1 2X+1 X X+2 2X+1 2X+1 2X+1 X 2 1 X+1 2X 2X+1 2X+2 2X 2X 2X+2 2X 1 2 1 X+2 1 X+1 2X+1 2 X+2 2X+1 X+2 2X 1 2X+1 2X 2X+1 2X+1 1 2 2X 2X+1 2X 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 X X+2 2X+2 2 2X+1 2 0 1 1 X+2 X 2X+1 X X+1 X+1 2 2 1 1 2X+2 0 2 2 0 2X+1 X+1 1 2 X+1 2X+2 X+1 0 X+1 1 2X+2 1 2X+2 2X+2 X 2X+2 0 2 1 0 X+1 X+1 2X+2 1 2X+2 2X 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 1 1 2X 2 0 X+1 0 X X+1 1 X+2 1 1 0 X 2 2X+1 2 2X+2 X+2 0 X 2X+2 2 X+1 X 2X+1 2 X+2 0 X 2X+2 X+2 X+2 2X X+2 0 2X+1 X+1 1 X+2 2X 2X 2X+1 2X 0 X 2X 2X+2 2X generates a code of length 93 over Z3[X]/(X^2) who´s minimum homogenous weight is 168. Homogenous weight enumerator: w(x)=1x^0+146x^168+210x^169+384x^170+778x^171+852x^172+1008x^173+1396x^174+1146x^175+1350x^176+2310x^177+1638x^178+1842x^179+2660x^180+2142x^181+2130x^182+2992x^183+2298x^184+2406x^185+3370x^186+2394x^187+2328x^188+3290x^189+2286x^190+2292x^191+2660x^192+1968x^193+1674x^194+2172x^195+1368x^196+1152x^197+1304x^198+702x^199+576x^200+636x^201+372x^202+258x^203+278x^204+78x^205+90x^206+58x^207+30x^208+6x^209+12x^211+4x^213+2x^219 The gray image is a linear code over GF(3) with n=279, k=10 and d=168. This code was found by Heurico 1.16 in 78.3 seconds.