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 X 1 1 X 1 1 1 1 1 1 1 X 1 X 1 X 1 1 1 1 1 1 1 0 X^2 0 0 0 0 0 0 0 0 X^2 2X^2 2X^2 X^2 X^2 X^2 0 2X^2 X^2 2X^2 X^2 0 X^2 0 2X^2 X^2 0 2X^2 X^2 2X^2 2X^2 2X^2 X^2 X^2 0 X^2 2X^2 2X^2 0 0 0 X^2 2X^2 X^2 X^2 X^2 0 2X^2 X^2 2X^2 X^2 0 X^2 2X^2 0 0 2X^2 2X^2 2X^2 0 X^2 2X^2 0 0 0 2X^2 0 2X^2 0 2X^2 2X^2 0 0 X^2 0 0 X^2 0 0 0 0 X^2 2X^2 2X^2 2X^2 0 0 2X^2 X^2 2X^2 X^2 0 X^2 X^2 0 2X^2 2X^2 0 X^2 X^2 2X^2 0 X^2 0 2X^2 2X^2 2X^2 X^2 0 2X^2 2X^2 2X^2 X^2 X^2 2X^2 2X^2 2X^2 2X^2 0 2X^2 0 2X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 2X^2 X^2 X^2 0 2X^2 0 X^2 X^2 X^2 0 0 0 0 2X^2 0 2X^2 0 0 0 0 X^2 0 0 X^2 2X^2 0 2X^2 0 0 2X^2 X^2 X^2 2X^2 0 X^2 0 2X^2 0 2X^2 2X^2 0 2X^2 0 X^2 2X^2 2X^2 X^2 X^2 X^2 2X^2 0 2X^2 0 2X^2 X^2 0 2X^2 X^2 2X^2 2X^2 X^2 X^2 X^2 X^2 2X^2 0 0 0 X^2 0 0 X^2 2X^2 X^2 2X^2 0 X^2 2X^2 X^2 X^2 0 0 X^2 0 0 2X^2 2X^2 0 2X^2 0 2X^2 0 0 0 0 X^2 0 2X^2 2X^2 X^2 0 2X^2 2X^2 2X^2 0 2X^2 2X^2 0 2X^2 X^2 0 2X^2 2X^2 0 X^2 2X^2 0 2X^2 X^2 0 X^2 0 X^2 0 2X^2 2X^2 0 0 2X^2 2X^2 X^2 0 X^2 2X^2 X^2 0 2X^2 2X^2 2X^2 X^2 X^2 X^2 0 X^2 0 2X^2 2X^2 X^2 X^2 2X^2 0 0 X^2 0 X^2 2X^2 2X^2 0 X^2 0 0 0 X^2 0 0 0 0 0 0 0 X^2 2X^2 2X^2 2X^2 2X^2 2X^2 2X^2 X^2 2X^2 X^2 X^2 2X^2 X^2 2X^2 2X^2 2X^2 2X^2 0 2X^2 0 X^2 0 0 2X^2 X^2 2X^2 0 2X^2 X^2 X^2 0 X^2 0 0 X^2 0 X^2 2X^2 X^2 2X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 2X^2 2X^2 2X^2 X^2 0 2X^2 0 0 X^2 X^2 0 0 X^2 X^2 X^2 2X^2 2X^2 X^2 0 2X^2 X^2 2X^2 generates a code of length 74 over Z3[X]/(X^3) who´s minimum homogenous weight is 135. Homogenous weight enumerator: w(x)=1x^0+48x^135+124x^138+118x^141+506x^144+394x^147+4374x^148+550x^150+280x^153+24x^156+38x^159+24x^162+24x^165+28x^168+8x^171+6x^174+4x^177+4x^180+4x^183+2x^207 The gray image is a linear code over GF(3) with n=666, k=8 and d=405. This code was found by Heurico 1.16 in 0.576 seconds.