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 X 1 1 1 X 1 1 0 2X^2 1 X 1 1 X 1 1 1 0 X 0 0 2X 2X^2+X 2X^2+2X X 2X 2X^2+X 2X^2 0 2X^2+X 2X^2+2X X^2 2X^2+2X 2X 2X^2+X 2X^2+X 2X^2+2X X^2+X 2X 2X^2+X 2X^2 2X^2 X^2+2X 2X^2 0 X^2+X 2X^2+2X 2X^2+2X 2X^2 X 2X X^2+2X X X X^2+X X 2X^2+2X X^2+2X X^2+2X 2X^2+2X 0 0 2X^2 2X^2 2X^2 2X^2+2X X 0 2X^2+2X X^2 2X X X^2+2X 2X^2+X X^2+2X 2X^2+X 2X^2 2X^2+X X 2X^2+2X X^2 X 0 X X^2+X X^2+2X 2X 0 X X^2 0 0 X 2X 0 X^2+2X X^2+X X X^2+2X 2X^2+2X X 2X^2 X^2+X X^2+X 2X 0 2X 2X^2 X^2+2X X^2+2X 2X^2 X^2 X^2+X X 0 X 2X^2+X 2X^2+2X X^2+2X X 2X^2 0 2X^2+X 2X^2+2X X^2+2X X^2+2X X^2 X^2+2X 2X^2+X X^2 2X 0 2X^2+X X^2+X 2X^2+2X X 2X^2 2X^2 X 2X^2 2X^2+2X 0 X^2+2X X^2+X X^2 2X^2+2X 2X^2 2X 2X^2+X 0 2X X 0 X 2X^2+X 2X X 0 2X^2 2X X^2 X^2+X 2X^2 0 0 0 X^2 0 0 2X^2 0 0 X^2 2X^2 X^2 2X^2 X^2 2X^2 X^2 X^2 0 0 2X^2 0 2X^2 2X^2 X^2 2X^2 0 0 X^2 2X^2 2X^2 0 X^2 X^2 X^2 X^2 2X^2 X^2 2X^2 2X^2 X^2 2X^2 2X^2 0 X^2 0 2X^2 2X^2 0 X^2 X^2 0 X^2 2X^2 X^2 X^2 2X^2 2X^2 0 X^2 2X^2 0 X^2 0 2X^2 X^2 0 2X^2 0 X^2 X^2 X^2 2X^2 X^2 0 0 0 0 X^2 2X^2 0 X^2 2X^2 0 2X^2 X^2 0 0 0 X^2 2X^2 X^2 X^2 2X^2 2X^2 X^2 X^2 X^2 0 X^2 X^2 2X^2 2X^2 2X^2 2X^2 2X^2 X^2 0 X^2 X^2 2X^2 0 2X^2 0 X^2 2X^2 0 2X^2 2X^2 0 2X^2 2X^2 X^2 0 X^2 2X^2 2X^2 2X^2 X^2 0 X^2 0 2X^2 X^2 X^2 0 2X^2 2X^2 X^2 2X^2 X^2 2X^2 X^2 0 0 2X^2 0 generates a code of length 73 over Z3[X]/(X^3) who´s minimum homogenous weight is 135. Homogenous weight enumerator: w(x)=1x^0+186x^135+138x^136+138x^137+544x^138+210x^139+198x^140+746x^141+1224x^142+336x^143+1994x^144+4098x^145+252x^146+3024x^147+4128x^148+216x^149+700x^150+144x^151+162x^152+312x^153+108x^154+66x^155+290x^156+72x^157+54x^158+128x^159+72x^160+24x^161+72x^162+12x^163+12x^164+8x^165+10x^168+2x^174+2x^201 The gray image is a linear code over GF(3) with n=657, k=9 and d=405. This code was found by Heurico 1.16 in 2.41 seconds.