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 1 1 1 2X 2X 2X 1 1 1 1 1 1 1 1 1 X 1 1 0 X 1 1 X 1 2X 0 1 2X 0 1 1 0 X 1 0 1 1 X 1 X 0 0 1 2X 1 2X 1 1 1 2X 1 1 2X 2X 1 1 1 2X 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 2 X X+2 2 2X 1 1 2 2X+2 2X+2 X+1 2 2X 0 X+1 0 1 2X+2 2X+1 X 1 2X 2 2X X+1 1 1 2X+2 1 X 0 X 1 2X 0 1 2X+1 2 X X+1 1 X 1 2X 1 2X+1 1 2X+1 0 2X+2 X X 0 1 1 X 1 2X+2 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 2 X+2 2 1 1 1 2 X+1 2X+2 2X+1 X+2 2X+1 X+1 2 X+1 X+1 2X+1 X+2 X+1 1 2X+1 2X+2 X+2 0 X+1 2X+1 2X X 1 1 1 2X+1 2 1 2 2 X+1 X+2 1 2 X+2 2X 2X+2 0 X+1 X+1 2X 2X 2X 1 2X X+2 X+2 0 2X+1 X+1 1 2 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 X+1 1 2X+2 2 2X+1 X+1 X+2 1 X+2 0 0 0 2X X 0 X+2 2X 2 X+1 2X+1 2 2X 1 1 X+1 X+2 2 0 X X+1 1 X X+1 2 1 2X+2 2 2X+2 X+2 X+2 1 2X+2 1 2X+2 2 2X 1 X+2 X 1 1 X+2 X 2X+1 X+1 1 2X+1 X+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 2X 1 0 X 1 X+2 1 X+2 X+2 1 0 2X+1 1 2 X 2X 1 X 2X 0 X 1 X+2 2 1 2X+1 2X+2 2X+1 1 2 2X X+1 X+2 X+2 2X+2 2 X 0 2X 1 X+1 2X+2 2X+2 X+1 2X X+1 X+1 X+2 1 2X+1 0 X+2 2 X+1 X 2 X+1 2X+2 2X+2 generates a code of length 91 over Z3[X]/(X^2) who´s minimum homogenous weight is 165. Homogenous weight enumerator: w(x)=1x^0+216x^165+408x^166+504x^167+1128x^168+948x^169+1164x^170+1678x^171+1374x^172+1590x^173+2210x^174+1854x^175+1998x^176+2750x^177+2280x^178+2316x^179+3610x^180+2346x^181+2298x^182+3250x^183+2292x^184+2526x^185+3232x^186+2112x^187+2004x^188+2354x^189+1632x^190+1506x^191+1954x^192+1302x^193+930x^194+1000x^195+624x^196+492x^197+476x^198+246x^199+150x^200+146x^201+66x^202+18x^203+44x^204+12x^205+8x^207 The gray image is a linear code over GF(3) with n=273, k=10 and d=165. This code was found by Heurico 1.16 in 86 seconds.