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 0 X 1 1 1 1 X 1 X^2 1 0 1 X^2 1 1 0 X 1 X^2 0 1 1 X 1 X X X 0 X 1 0 1 X^2 0 1 1 X^2 0 X 0 0 0 X X^2+X X 0 X^2 X^2 0 X X^2+X X X^2+X X^2+X X^2+X X^2+X X^2 0 0 X^2+X X^2 0 X^2 X X X^2+X X^2 X^2+X X^2+X X X^2 X^2 X X 0 X X 0 X^2+X 0 X X 0 X X X^2 0 0 X^2+X X 0 X X^2+X X^2+X X^2+X X^2+X X X^2 X^2 0 X^2+X X^2+X 0 X^2 0 X^2 X^2+X X^2 X^2 0 0 X 0 X X X^2+X 0 0 0 X^2+X X^2+X X X X^2 0 X X^2 0 X^2+X X^2+X X^2 X^2+X X^2 X^2+X 0 X^2 X^2 X^2+X X^2+X 0 0 X^2+X X^2 0 X^2+X X^2 X^2+X X^2+X X^2 0 X X X^2 X^2 X X^2+X X^2 X 0 0 X^2+X 0 0 0 X^2 X 0 X^2 0 X^2+X X X 0 X^2 X X 0 0 0 X^2+X X^2 0 0 0 X X 0 X^2+X X X^2 X^2+X X X^2 X^2 X X X^2 0 X^2+X 0 X X^2 X X 0 X^2 X 0 X^2+X X X X^2+X X^2+X X^2 0 0 X X X 0 X^2+X X X^2+X X^2+X X^2+X X 0 X X X^2 X^2+X X X X^2 X X^2 X^2+X 0 X^2+X X 0 X^2 0 X^2+X X^2 X^2 0 X^2+X X X X^2 0 0 0 0 0 0 X^2 0 0 0 X^2 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 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 0 X^2 X^2 0 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 0 X^2 0 0 0 X^2 0 0 0 0 0 0 0 0 X^2 0 X^2 0 0 X^2 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 0 0 0 0 X^2 X^2 0 X^2 0 0 X^2 0 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 0 X^2 0 0 0 0 0 0 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 generates a code of length 72 over Z2[X]/(X^3) who´s minimum homogenous weight is 64. Homogenous weight enumerator: w(x)=1x^0+300x^64+212x^66+663x^68+552x^70+822x^72+512x^74+480x^76+208x^78+231x^80+28x^82+47x^84+24x^86+13x^88+2x^92+1x^104 The gray image is a linear code over GF(2) with n=288, k=12 and d=128. This code was found by Heurico 1.16 in 78.5 seconds.