The generator matrix 1 0 1 1 1 X^2+X 1 1 0 X^2+X 1 1 1 X^2 1 1 X 1 1 1 X^2 1 X 1 1 1 X 1 X X^2+X 1 0 1 X 0 1 1 1 1 X^2 1 1 1 1 X^2+X X 1 1 X 1 X^2+X 1 1 X^2+X 1 1 0 1 1 X^2 1 X^2 1 X 1 0 1 1 1 1 1 X X 1 0 1 1 0 1 1 X X^2+X+1 1 1 X^2+X+1 X^2+X 1 1 0 X 1 X^2+1 X^2 X+1 1 X 1 1 X^2+X+1 X^2+X 1 X^2 1 1 1 1 X 1 1 X^2+1 X^2 1 X^2+1 1 X^2+X X^2+X+1 X X^2 1 1 1 1 1 X^2+X+1 1 X^2+X X^2 1 0 X^2+X+1 1 X^2 X^2+X+1 1 X 1 1 1 1 X X^2 X X+1 X^2+X+1 X^2+X 1 0 X^2+X+1 0 0 X 0 0 0 0 0 0 X^2 0 0 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2+X X^2+X X X X X^2+X X X^2+X X X X X^2+X X^2 X^2+X X^2+X X X X^2 X X^2+X X^2+X X X X X X^2+X X X^2 X^2+X X^2+X X^2 X X X X^2+X X^2 X^2+X X^2 X^2 0 0 X^2+X X^2 0 X^2 0 0 0 X^2 X^2+X 0 0 0 0 X 0 0 X X^2 X X^2+X X X^2 X^2+X X X X^2 0 X 0 0 X^2 X^2+X X X^2+X X^2+X X X^2 X^2 X^2+X 0 X 0 X^2 X^2+X 0 X^2 X X^2 X^2 X X X^2+X X^2+X 0 X X^2 X 0 X X 0 0 X X^2+X X 0 X^2+X X X^2+X X^2+X X^2 X^2+X 0 X X^2+X X^2 X^2+X X^2 X^2+X X^2 X^2+X X^2+X X X^2 0 0 0 0 X 0 0 X X X^2+X X^2 X^2 X^2 X^2 X^2+X X^2+X X X^2+X X X^2 X X 0 X X^2+X 0 0 X^2 0 X X^2 X 0 X^2+X 0 0 X X^2+X X^2 X^2 0 0 0 X^2+X X^2+X X X^2 X^2 0 X^2+X X X^2+X X^2 X 0 X^2+X 0 X^2+X 0 X^2+X X^2 X^2 0 X X X 0 X^2+X X^2 X^2 0 0 X X^2+X 0 0 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 0 0 X^2 0 0 0 X^2 0 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 0 X^2 generates a code of length 74 over Z2[X]/(X^3) who´s minimum homogenous weight is 65. Homogenous weight enumerator: w(x)=1x^0+44x^65+164x^66+206x^67+347x^68+480x^69+588x^70+732x^71+608x^72+622x^73+716x^74+696x^75+706x^76+666x^77+484x^78+340x^79+294x^80+184x^81+98x^82+58x^83+37x^84+36x^85+15x^86+16x^87+20x^88+14x^89+13x^90+2x^92+2x^93+1x^94+1x^96+1x^98 The gray image is a linear code over GF(2) with n=296, k=13 and d=130. This code was found by Heurico 1.16 in 5.43 seconds.