The generator matrix 1 0 0 1 1 1 1 1 1 1 2X^2 1 X 1 2X^2 1 1 1 1 1 2X^2+2X 1 1 2X^2 2X^2+X 1 2X^2+X 1 1 2X^2+2X 1 1 1 1 1 0 1 1 0 2X^2+2X 1 X 1 1 0 1 1 1 1 1 2X^2 1 1 1 2X^2+X 2X 1 1 1 1 1 1 1 2X^2 1 2X^2+2X 2X^2+2X 1 2X^2+X 1 1 1 1 0 1 0 0 X^2 2X^2+2X+1 2X^2+2X+1 X+2 1 2X^2+X+2 1 2X^2+2 1 X^2 1 X+1 X+2 2X^2+2 2 2X^2+X 1 1 X^2+2X 2X^2+2X 1 X^2+1 1 X^2+2X 2X^2+X+1 1 0 X^2+2X 2X^2+2X+1 2X^2+X+2 2X+2 2X^2+2X X^2+2 2X^2+2X+2 2X^2+X 1 2X+2 1 2X^2+1 2X 1 X^2+2X+1 2X^2+1 2X^2+1 X^2+X 2X^2+X 2X^2 X^2+2 X+1 X^2+2X+1 X^2+2X 1 2X^2+X 0 X^2+2X+2 2X^2+X+2 2X+2 0 X+2 1 X^2+2X 2X 1 2 1 2X+2 X^2 2X^2 X 0 0 1 1 2X^2+2 2X^2+2 2X^2+2X 1 X^2+1 2X^2+2X 2X^2+1 2X^2+X+2 X+2 0 2X^2+2X+1 X^2 X^2+X 2X^2+2 X^2+2X+1 X+2 2X^2+X+2 2X+2 X^2+X+1 1 2X^2+2X X+1 2X^2+X+2 1 2X^2+X X^2 2X^2+2 2X^2 X^2+X+1 X+2 2X^2+X 1 2X^2+X+1 2X^2+2X+2 1 X^2+X+1 2X^2+X+1 1 2X^2+X+2 X^2+2 X^2 2X^2+1 2X^2 2X^2+2X+1 2 X^2+2X+1 1 X X^2+X+2 2X^2+1 1 1 2X^2 X^2+2X+2 2X^2+2X+1 2X X^2+2X+2 2X^2+X 2X^2+1 2X 2X^2+2X+2 1 X+1 2X^2 2X^2+2X+1 2X^2+2X+2 X^2+2X+2 2X^2+X+1 2X^2+X 0 0 0 2X 2X^2 X^2 0 X^2 0 2X^2 2X^2 2X^2 0 X 2X^2+2X 2X^2+2X 2X^2+2X X^2+2X 2X X^2+X X^2+X 2X^2+2X 0 2X^2+2X X X^2+2X 2X X X^2+X 2X^2+2X 2X^2+2X 2X X 2X 2X^2 2X^2+X 2X^2+X X X^2 2X 2X^2+2X X^2+X X^2+X 2X^2+2X 2X^2+2X 2X^2+X 2X^2+X 2X X^2 2X^2 2X^2+2X 2X X^2 X^2 2X^2+X 2X^2+X 2X^2+2X X^2 X^2 X^2+X 0 0 2X^2+X X^2+X X^2+X X 2X^2+X 0 2X^2+X X^2 2X 2X 2X 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+374x^135+474x^136+2166x^137+3284x^138+3774x^139+7308x^140+8408x^141+8670x^142+13734x^143+14350x^144+12504x^145+19890x^146+17402x^147+13746x^148+17406x^149+12028x^150+7302x^151+6840x^152+3906x^153+1386x^154+1062x^155+562x^156+180x^157+60x^158+114x^159+48x^160+36x^161+62x^162+12x^163+12x^164+10x^165+12x^166+12x^167+6x^168+6x^172 The gray image is a linear code over GF(3) with n=657, k=11 and d=405. This code was found by Heurico 1.16 in 76.9 seconds.