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 0 X 1 X X X X 1 X^2 1 X^2 0 X 0 1 1 0 X^2 X 1 1 X 0 1 0 0 1 1 0 X^2 1 X 0 1 1 X^2 X^2 0 X 0 0 0 X X^2+X X 0 X^2 X^2 X X^2+X 0 X^2+X X X^2 X^2+X X^2+X 0 0 X X^2+X X^2+X 0 0 X^2+X X X^2 0 0 X X X X 0 X 0 X^2 X X X X^2 0 X X^2+X X^2+X X X X X^2 X^2 X^2 X^2 X X X^2 0 X X X X X^2+X 0 X X^2 0 X X X 0 X X^2+X 0 0 0 0 0 X 0 X X X^2+X 0 0 0 X X^2 X X^2+X X^2 X^2+X X^2 X^2 X^2 0 X X X^2 X^2+X X^2 X X X^2 X X^2+X 0 X X^2+X X^2+X X^2+X 0 X^2+X X X X^2 X X^2+X 0 X^2+X 0 0 X X^2 X^2 X X^2 X X X^2+X 0 X^2+X X X X^2+X 0 X^2+X 0 X^2 X X X^2+X X X^2+X X^2 X^2+X X^2 0 0 0 X 0 0 0 0 X X 0 X^2+X X 0 X 0 X X^2+X X^2+X X^2 X^2 0 X^2 X X^2+X 0 0 X^2+X X^2+X X 0 X 0 X X 0 0 X^2 X^2 X X^2 0 X^2 X 0 X^2 X X X^2 X^2+X 0 X^2 X^2+X X^2+X X^2 X X^2 0 X^2+X X^2 X X X^2+X X^2 X^2 0 X^2 X^2 X^2+X X X 0 X X^2 X^2+X X^2+X 0 X 0 X^2+X X^2 0 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 0 0 X^2 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2 0 X^2 X^2 X^2 0 0 0 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 0 0 X^2 0 0 0 0 0 0 0 X^2 X^2 0 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 0 0 0 X^2 0 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 0 0 X^2 0 X^2 0 0 0 0 X^2 0 0 0 0 0 0 0 X^2 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 0 0 0 X^2 X^2 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 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 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 0 X^2 0 0 X^2 0 X^2 0 0 0 0 0 0 0 X^2 0 0 0 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 X^2 0 0 0 X^2 X^2 0 0 0 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 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 0 0 0 0 X^2 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 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 0 X^2 X^2 0 X^2 0 0 X^2 X^2 0 0 X^2 0 X^2 X^2 0 0 0 0 X^2 0 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 0 generates a code of length 76 over Z2[X]/(X^3) who´s minimum homogenous weight is 64. Homogenous weight enumerator: w(x)=1x^0+184x^64+8x^65+360x^66+20x^67+748x^68+144x^69+878x^70+304x^71+1528x^72+640x^73+1652x^74+1000x^75+1744x^76+848x^77+1682x^78+608x^79+1350x^80+376x^81+908x^82+100x^83+613x^84+32x^85+334x^86+16x^87+177x^88+72x^90+46x^92+2x^94+7x^96+1x^100+1x^104 The gray image is a linear code over GF(2) with n=304, k=14 and d=128. This code was found by Heurico 1.16 in 25.7 seconds.