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 X^2 1 1 1 1 1 1 1 1 1 1 1 1 X^2 1 1 X^2 1 1 X 0 X 0 X^2+X 0 X^2+X 0 X^2+X 0 X^2+X X^2 X^2+X 0 X^2+X X X^2 0 X^2+X X X^2 X^2 X^2+X X 0 0 X^2+X 0 X X^2 X^2 X^2+X X^2+X X 0 X 0 X^2+X X^2 X^2+X 0 X^2+X X X^2 X^2 X^2 X X^2+X 0 0 X^2+X 0 X X^2 X 0 0 X^2+X 0 X^2+X 0 X^2 X X^2 X^2+X X^2+X X^2 X X^2 X^2 0 X^2 X^2+X 0 0 X^2 0 0 0 0 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 0 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 0 X^2 0 X^2 0 0 X^2 0 0 X^2 0 0 X^2 0 0 0 0 0 X^2 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 0 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 0 0 0 X^2 0 X^2 X^2 X^2 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 X^2 0 0 X^2 0 X^2 0 0 X^2 0 X^2 X^2 X^2 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 0 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 0 X^2 0 0 X^2 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 0 0 0 0 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 0 0 0 generates a code of length 72 over Z2[X]/(X^3) who´s minimum homogenous weight is 66. Homogenous weight enumerator: w(x)=1x^0+52x^66+125x^68+201x^70+64x^71+182x^72+128x^73+85x^74+64x^75+43x^76+27x^78+28x^80+19x^82+4x^84+1x^136 The gray image is a linear code over GF(2) with n=288, k=10 and d=132. This code was found by Heurico 1.16 in 12.7 seconds.