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 X 1 1 1 X 1 1 X 1 1 1 X 1 X 1 1 1 1 1 X 1 1 1 1 1 1 1 1 1 1 0 X 0 0 0 0 0 0 0 0 X 2X 2X X X X 0 2X X 2X X 0 X 0 2X X 0 2X X 2X 2X 2X X X X 0 2X 2X 0 0 X 0 2X X 0 X 2X 2X X 2X 2X 2X X 2X X X 0 2X X X 2X 0 X 0 X 2X 0 0 2X X 0 X X X 2X 2X X 0 X X 0 X 0 0 0 2X X X 0 0 0 X 0 0 0 0 X 2X 2X 2X 0 0 2X X 2X X 0 X X 0 2X 2X 0 X X 2X 0 X 0 2X 2X 2X X 2X 0 2X 2X X 2X 2X X 2X 2X 0 2X 0 2X 0 X 0 2X 0 X 2X 0 X X X 0 X 2X X 0 X 0 X X 2X X 0 0 2X X 2X X 0 2X X 2X 2X X 0 X 2X X 2X 2X 0 0 0 0 X 0 0 X 2X 0 2X 0 0 2X X X 2X 0 X 0 2X 0 2X 2X 0 2X 0 X 2X 2X X X X 2X 0 0 2X 2X X 2X X 2X 0 2X X X X 2X 2X 2X 0 X 2X 0 X X 0 0 X X X X X 2X X X X 2X 2X 2X 2X X 2X 2X 2X 2X 0 X X X X 2X 0 2X X 2X X X 0 0 0 0 0 0 X 0 2X 2X X 0 2X 2X 2X 0 2X 2X 0 2X X 0 2X 2X 0 X 2X 0 2X X 0 X 0 X 0 2X 0 2X 0 2X X 0 X 2X 2X X 2X 2X 0 2X 0 X X 0 X X X X 0 X 0 2X 2X X 0 0 X 0 2X X X X X X 2X X X 2X X 0 0 2X 2X 2X X 0 0 X X 2X 2X 0 0 0 0 0 X 2X 2X 2X 2X 2X 2X X 2X X X 2X X 2X 2X 2X 2X 0 2X 0 X 0 0 2X X 2X 0 2X X 0 X X 0 X 0 X 0 2X X X X X 0 X X 2X 2X X X 0 2X X 0 2X 2X X 2X X X X X X 0 2X 2X X 2X X X X 2X X 2X 0 2X X 2X 2X X 0 2X 2X 0 0 generates a code of length 89 over Z3[X]/(X^2) who´s minimum homogenous weight is 165. Homogenous weight enumerator: w(x)=1x^0+58x^165+120x^168+30x^169+82x^171+120x^172+124x^174+300x^175+76x^177+510x^178+58x^180+366x^181+46x^183+132x^184+30x^186+22x^189+26x^192+32x^195+14x^198+10x^201+6x^204+8x^207+4x^210+4x^213+4x^216+2x^219+2x^249 The gray image is a linear code over GF(3) with n=267, k=7 and d=165. This code was found by Heurico 1.16 in 0.319 seconds.