The generator matrix 1 0 1 1 1 X^2+X 1 1 0 1 1 X^2+X 1 X^2+X 1 1 0 1 1 1 0 1 X^2+X 1 1 1 0 1 X^2+X 1 1 1 1 1 0 1 X^2+X 1 1 0 1 1 X^2+X 0 1 X^2+X 1 X^2 1 1 X X^2+X 1 0 1 X^2 1 X^2+X 1 1 1 1 1 X X X^2+X X^2+X X 1 X^2 0 1 1 1 0 1 X+1 X^2+X 1 1 0 X+1 1 X^2+X X^2+1 1 X^2+X 1 X+1 0 1 X^2+1 0 X^2+1 1 X^2+X 1 X+1 X+1 X^2+1 1 0 1 X^2+X X^2+1 0 X+1 X^2+X 1 X^2+X 1 X X+1 1 X^2+X+1 X^2+X 1 1 X^2+1 1 0 1 X^2+X X^2+1 1 1 X+1 1 X 1 X+1 1 X^2+1 X^2+X+1 X+1 X^2+X X 0 1 1 1 1 0 X^2 1 X^2+1 X+1 X+1 0 0 X^2 0 0 0 0 0 0 0 0 0 0 0 X^2 0 X^2 0 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 0 0 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 0 0 0 0 0 X^2 X^2 X^2 0 0 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 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 X^2 0 X^2 X^2 X^2 0 0 0 0 0 X^2 0 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 0 0 0 X^2 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 0 0 0 0 X^2 0 0 0 X^2 0 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 0 0 X^2 0 0 X^2 X^2 X^2 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 X^2 0 X^2 X^2 0 0 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 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 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 0 0 X^2 X^2 0 0 0 X^2 0 X^2 0 X^2 0 X^2 0 0 0 0 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 0 0 0 0 0 0 0 0 0 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 0 X^2 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 X^2 0 0 0 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 0 0 0 0 0 X^2 0 X^2 0 X^2 X^2 0 X^2 generates a code of length 74 over Z2[X]/(X^3) who´s minimum homogenous weight is 61. Homogenous weight enumerator: w(x)=1x^0+6x^61+55x^62+32x^63+131x^64+188x^65+242x^66+448x^67+438x^68+954x^69+723x^70+1580x^71+1008x^72+1888x^73+1062x^74+1944x^75+965x^76+1586x^77+737x^78+944x^79+376x^80+452x^81+179x^82+168x^83+103x^84+46x^85+38x^86+4x^87+32x^88+20x^90+11x^92+14x^94+4x^96+1x^98+3x^100+1x^102 The gray image is a linear code over GF(2) with n=296, k=14 and d=122. This code was found by Heurico 1.16 in 43.7 seconds.