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 2X 1 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 2X 1 1 1 0 1 1 1 1 2X 0 2X 1 1 2X 2X 1 X 1 1 2X 1 1 1 0 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 1 2 2X+2 1 X 2X+2 2 2 X+1 1 1 1 2 1 0 1 X+1 X X+2 2X+2 1 2X+1 1 2 X 1 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 2 X+1 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+1 X+2 0 1 1 X 2X+2 X+1 X+2 2X X+2 2 X 0 1 1 2 1 2X+1 2X+2 2 X+1 2X+1 2X+1 2X 2X+2 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 2X X+1 2 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 2X 0 0 2X X+2 2X+2 0 2X+1 X X+1 0 0 X+1 X+2 1 X+2 1 2X+1 X 2X+1 0 2 1 0 1 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 X+1 2X+2 2X+2 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 1 X 2 2 X 2X 2 2X+2 1 X 2X 2X+2 2X+1 X+2 X+1 X 2X X+2 2X X+1 0 X+2 X 2X+1 X+2 2X+1 generates a code of length 90 over Z3[X]/(X^2) who´s minimum homogenous weight is 163. Homogenous weight enumerator: w(x)=1x^0+312x^163+474x^164+490x^165+846x^166+1158x^167+1054x^168+1566x^169+1686x^170+1322x^171+2184x^172+2364x^173+1720x^174+2382x^175+2700x^176+2036x^177+2802x^178+3012x^179+2038x^180+3240x^181+2994x^182+2116x^183+2904x^184+2784x^185+1706x^186+2604x^187+2190x^188+1452x^189+1686x^190+1422x^191+804x^192+852x^193+690x^194+416x^195+372x^196+288x^197+110x^198+84x^199+90x^200+36x^201+36x^202+12x^203+6x^204+6x^206+2x^222 The gray image is a linear code over GF(3) with n=270, k=10 and d=163. This code was found by Heurico 1.16 in 99.3 seconds.