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 X 1 1 1 X 1 1 1 1 1 1 1 X 1 X 1 1 1 X 1 1 1 1 0 X^2 0 0 0 0 0 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2 0 X^2 X^2 0 0 0 0 0 X^2 0 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 X^2 0 0 X^2 0 0 0 X^2 0 0 0 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 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 0 0 X^2 0 X^2 0 0 0 X^2 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 0 0 0 0 X^2 0 0 0 0 X^2 0 0 X^2 0 X^2 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 0 0 X^2 0 X^2 X^2 0 0 0 0 0 0 0 X^2 0 X^2 X^2 0 0 X^2 0 X^2 X^2 0 0 0 0 0 X^2 0 0 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 0 0 0 X^2 0 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 0 0 0 0 0 0 X^2 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 0 0 0 X^2 X^2 0 0 0 0 0 X^2 X^2 X^2 0 0 0 X^2 0 0 0 0 0 0 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 0 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2 0 0 X^2 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 0 0 X^2 X^2 X^2 0 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 generates a code of length 68 over Z2[X]/(X^3) who´s minimum homogenous weight is 60. Homogenous weight enumerator: w(x)=1x^0+31x^60+36x^62+8x^63+38x^64+40x^65+20x^66+80x^67+537x^68+80x^69+26x^70+40x^71+20x^72+8x^73+22x^74+7x^76+15x^78+5x^80+6x^82+1x^84+2x^86+1x^126 The gray image is a linear code over GF(2) with n=272, k=10 and d=120. This code was found by Heurico 1.16 in 0.252 seconds.