The generator matrix 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 X X X 1 1 X 1 1 1 1 1 1 X X 1 1 1 1 1 0 X 0 0 2X 2X^2+X X 2X^2+2X 2X X^2 2X^2 2X^2+X 2X^2+X 2X^2+2X 2X 2X^2 X^2+X 2X^2+2X X 2X^2+X X 2X X^2 X^2+2X 0 2X^2+X 2X^2+2X X X 2X^2 2X^2 X^2 X^2+X X^2+X X^2+2X X^2+2X 0 X^2 2X^2+X X^2+2X X^2+2X X X^2 X^2+2X 2X^2+2X 0 X^2+2X X^2 0 2X 2X 2X^2+X 2X^2 X^2+X 0 X^2+2X 2X^2+X X^2+X X 2X X^2+2X 2X 2X X^2+2X X X^2 2X^2 0 X^2 0 X X^2 2X^2+2X 2X^2+X X^2 X^2+X 2X 0 X^2+2X 2X^2 2X^2+X 2X X^2 0 2X^2+X X^2+2X X^2+2X 2X X 0 X^2+X 0 0 X 2X X^2 2X^2+2X X 2X^2+X X^2+2X 2X^2+2X 0 2X^2+2X X^2 2X X^2 X X X^2+X 2X 0 X^2+X 2X 2X^2+2X X^2+X X^2+X 0 2X^2 2X^2+2X X 0 2X^2+2X X^2 2X^2+X 2X^2 X^2+2X X X^2+2X 2X^2+X X^2+2X 2X^2 X^2+X X^2+X 2X^2 2X^2 2X^2+2X X^2+2X X^2 X^2 X^2+X X^2+2X X 2X^2 X^2+X 2X^2+X 0 X^2+2X X^2+2X X^2+2X 2X^2+2X 2X^2+2X 2X^2+X 2X^2 0 0 2X^2+X X^2+X 2X^2 X 2X^2 X X^2 X 2X^2+X 2X^2+2X X X 0 2X 2X^2 2X^2 X X^2+X X 2X^2 2X^2 X 0 2X^2 0 2X 2X 0 0 0 X^2 0 0 0 0 0 0 2X^2 X^2 2X^2 X^2 2X^2 2X^2 X^2 2X^2 2X^2 X^2 2X^2 2X^2 2X^2 X^2 X^2 2X^2 X^2 2X^2 2X^2 X^2 X^2 0 X^2 2X^2 2X^2 2X^2 2X^2 X^2 0 2X^2 0 0 X^2 X^2 0 0 0 2X^2 2X^2 X^2 X^2 0 0 0 2X^2 0 X^2 2X^2 0 X^2 2X^2 2X^2 0 X^2 X^2 2X^2 0 X^2 0 0 2X^2 2X^2 0 X^2 X^2 0 2X^2 X^2 0 X^2 2X^2 X^2 0 0 0 X^2 2X^2 0 2X^2 2X^2 0 generates a code of length 91 over Z3[X]/(X^3) who´s minimum homogenous weight is 174. Homogenous weight enumerator: w(x)=1x^0+110x^174+198x^175+186x^176+326x^177+390x^178+456x^179+482x^180+840x^181+720x^182+862x^183+756x^184+474x^185+250x^186+78x^187+48x^188+52x^189+66x^190+12x^191+46x^192+48x^193+24x^194+28x^195+36x^196+18x^197+24x^198+12x^199+6x^200+2x^201+6x^202+2x^207+2x^249 The gray image is a linear code over GF(3) with n=819, k=8 and d=522. This code was found by Heurico 1.16 in 0.753 seconds.