The generator matrix 1 0 0 0 1 1 1 1 1 1 1 X^2 0 X^2+X X^2 0 0 1 1 0 X 0 1 1 X^2+X X^2+X 1 1 X^2+X 1 1 0 X^2 1 X^2+X 1 1 1 X^2 1 X 1 1 1 X^2+X 1 0 1 1 X^2+X 1 X X^2 1 1 1 0 1 0 X^2+X 0 1 X^2+X X^2+X 1 1 X^2+X 1 1 0 1 0 1 0 0 0 0 1 X^2+X+1 1 1 X^2+X 1 1 X 1 0 X X+1 X 1 1 1 X^2+X+1 X^2+1 1 X^2+X X X^2+X X X^2 X 1 1 X+1 0 0 X^2+1 X+1 X^2+X X^2+X 1 X^2+X+1 X X^2+X 1 1 1 X^2 1 1 X+1 X^2 X^2 0 X+1 0 X^2 0 0 X^2 1 0 X^2+X 1 X^2+X X 1 X^2+X+1 0 1 0 0 0 1 0 0 1 0 1 X^2+1 X^2 1 X^2+X+1 X+1 1 X^2 X 1 X^2+X+1 X+1 X^2+1 X^2 X+1 X^2+X X+1 X^2+X 0 X^2+X 0 1 1 X^2+1 X^2+X X X+1 1 0 X+1 X^2 1 X^2 X^2+X+1 1 1 0 X 0 1 X^2+X X X+1 X^2+X+1 1 1 X^2+X+1 X^2 1 X^2 X^2+1 0 1 X^2+X+1 X^2 1 X^2+1 X+1 X^2+X+1 X X^2 X 1 0 0 0 0 1 1 X+1 X^2+X+1 X^2+1 X^2 X X^2+X X^2+1 0 X^2+X+1 1 1 1 X+1 X^2+X+1 X^2+X X^2+1 X+1 X^2 X^2+X X 1 X^2+X+1 X^2 X^2+X X^2 X^2 1 X^2 X X^2+X X^2+1 X^2+X+1 X+1 X^2+1 X^2+X 0 X^2+1 X^2+X+1 X^2+1 X^2 X^2+X X 1 X^2+1 1 1 1 X^2+X X X^2 X+1 1 X+1 1 X+1 X X^2+X 1 X X^2+1 X^2 X X^2+1 1 X+1 X^2 0 0 0 0 X X X X 0 0 0 X^2+X X^2 X^2+X X^2+X X X^2+X X X^2+X X^2 X X X^2 X^2 X^2 X^2+X X^2+X X^2+X X^2+X X^2+X X 0 X^2+X X^2+X X^2+X 0 0 X^2 0 X^2+X X^2+X 0 0 X^2 X^2+X X^2+X X^2+X X X^2 0 X^2+X X 0 0 X^2+X X^2+X 0 X^2 X^2+X X^2 X X^2 X X^2+X X^2 0 0 0 0 X^2+X X^2 0 0 0 0 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 0 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 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 0 0 0 0 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 0 generates a code of length 71 over Z2[X]/(X^3) who´s minimum homogenous weight is 61. Homogenous weight enumerator: w(x)=1x^0+58x^61+428x^62+442x^63+1217x^64+1000x^65+2195x^66+1654x^67+2726x^68+1884x^69+3633x^70+2308x^71+3602x^72+1982x^73+3162x^74+1488x^75+1938x^76+900x^77+1066x^78+376x^79+356x^80+122x^81+131x^82+56x^83+16x^84+6x^85+9x^86+10x^87+2x^91 The gray image is a linear code over GF(2) with n=284, k=15 and d=122. This code was found by Heurico 1.16 in 45.8 seconds.