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 X X X 0 X 0 X X X X X^2 X^2 1 1 1 1 1 X 1 0 X 2X 0 2X^2+X 2X X^2 2X^2+X X^2+2X X^2 X^2+X X^2+2X X^2 0 X^2+X X 2X X^2+2X 2X^2 2X^2 2X^2+X X^2+X 2X^2+2X 2X^2+2X 2X^2 X 2X^2+2X 2X^2+X 2X 2X^2+X X 2X X X^2+X X^2+2X X^2+X X^2+2X X X 0 0 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 2X^2 2X^2 2X^2 X^2 0 X^2 0 X^2 0 2X^2 X^2 2X^2 0 2X^2 0 X^2 0 2X^2 X^2 2X^2 2X^2 X^2 0 2X^2 0 X^2 0 X^2 X^2 0 2X^2 2X^2 X^2 X^2 0 0 X^2 X^2 0 2X^2 0 2X^2 generates a code of length 46 over Z3[X]/(X^3) who´s minimum homogenous weight is 90. Homogenous weight enumerator: w(x)=1x^0+362x^90+252x^93+90x^96+20x^99+4x^108 The gray image is a linear code over GF(3) with n=414, k=6 and d=270. This code was found by Heurico 1.16 in 0.105 seconds.