The generator matrix 1 0 0 1 1 1 X^2+X 1 1 X^2 X 1 X^2+X 1 1 X^2+X X^2+X 1 1 X X 1 1 X^2 1 X 1 1 0 1 1 1 0 1 1 1 1 X 0 X^2+X 1 X X 1 X^2+X 1 1 1 1 1 0 1 X X^2+X 1 1 X^2 1 0 X 1 0 X^2 X^2+X X^2+X X 1 1 1 0 1 0 0 1 1 1 0 X^2 1 1 X^2+1 X^2+X 1 X 1 X 1 0 1 X^2 1 X 1 1 1 X^2+X+1 X^2 1 X X+1 X^2+X+1 1 X^2+X X^2+X+1 X 1 X 1 X^2 X^2+X 1 1 X^2+X+1 1 X^2+1 X 0 X^2+X+1 0 1 X^2+X+1 X^2 X^2+X X^2+X X 1 1 1 0 X X^2 1 1 1 1 X^2+X X^2+1 X+1 0 0 1 1 1 0 1 X+1 0 1 X^2 0 1 X^2+1 X+1 X^2+X+1 1 X^2+X 0 X 1 X+1 X+1 X^2+X+1 X+1 X X^2+X X X^2 X 1 X^2 1 X^2+1 X+1 X^2+X 1 1 X^2+1 1 X^2 X^2 X+1 X^2+X X X^2+X+1 X^2+1 X^2+X X^2+X+1 X^2+1 0 0 1 1 0 1 X+1 X^2 1 X X+1 1 X^2+1 X^2+X X^2+1 X^2+1 X^2+X+1 X^2+X+1 X^2+1 0 0 0 X 0 0 0 X^2 X X^2+X X X X X^2+X 0 0 X^2+X X^2+X X^2 X^2 X^2 X X^2+X X X^2 X^2+X 0 X^2+X 0 X^2 X^2 X 0 X^2+X X^2+X X X X 0 X X^2+X 0 X^2+X 0 X X 0 0 X X^2+X X X X 0 X X^2+X X^2+X X X^2+X X^2 X^2+X X^2 X^2+X X^2+X X^2+X X^2+X X^2 0 X^2 0 0 0 0 X 0 0 0 0 0 0 0 0 X^2+X 0 0 0 0 0 0 0 X^2+X 0 0 X^2+X X^2+X X X X^2+X X X^2 X^2+X X^2+X X^2+X X^2 X^2+X X^2 X^2+X X^2 X^2 X^2 X X X^2 X^2+X X^2 X X X^2+X X^2 X^2+X X X^2 X^2 X^2+X X X X X^2 X X^2+X X 0 X^2+X X^2+X X^2 X X^2 X^2+X 0 0 0 0 0 X X^2+X X^2 X^2 X X^2 X X^2 0 X^2+X X^2 X X^2 X^2+X X^2+X X X X^2+X X^2 X^2+X X^2 X 0 X^2+X X^2 X^2+X X X^2 X^2 X^2 X^2+X X^2+X X X^2 X X 0 X^2 0 X^2+X X X X^2+X 0 X^2 0 X X^2 X^2 0 X^2 X^2+X X^2 X X X^2+X X^2+X 0 X^2+X 0 X^2 X^2+X X^2 X^2 generates a code of length 69 over Z2[X]/(X^3) who´s minimum homogenous weight is 59. Homogenous weight enumerator: w(x)=1x^0+124x^59+388x^60+614x^61+872x^62+1196x^63+1598x^64+2066x^65+2471x^66+2644x^67+2780x^68+3166x^69+2943x^70+2686x^71+2675x^72+2098x^73+1469x^74+1060x^75+781x^76+420x^77+265x^78+204x^79+90x^80+76x^81+40x^82+20x^83+7x^84+8x^85+4x^86+2x^87 The gray image is a linear code over GF(2) with n=276, k=15 and d=118. This code was found by Heurico 1.16 in 70.8 seconds.