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 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X 1 1 1 0 X^2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 X^2 X^2 0 X^2 X^2 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 0 0 0 0 0 0 0 0 X^2 X^2 0 X^2 X^2 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 0 X^2 0 X^2 0 0 X^2 X^2 0 0 0 X^2 X^2 0 0 0 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 0 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 0 0 0 0 0 0 0 0 0 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 0 0 0 0 X^2 X^2 0 0 0 0 X^2 X^2 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 0 0 0 0 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 0 0 0 0 X^2 X^2 0 0 0 0 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 0 0 0 0 0 0 0 X^2 X^2 0 X^2 X^2 0 0 0 0 0 0 X^2 X^2 0 0 0 generates a code of length 78 over Z2[X]/(X^3) who´s minimum homogenous weight is 72. Homogenous weight enumerator: w(x)=1x^0+26x^72+68x^76+320x^78+73x^80+20x^84+3x^88+1x^152 The gray image is a linear code over GF(2) with n=312, k=9 and d=144. This code was found by Heurico 1.16 in 0.266 seconds.