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 X X^2 X 0 1 X 0 X X X 0 0 1 1 0 1 X^2 X^2 0 1 X 1 X X^2 1 X 1 1 X 1 X 1 0 X 1 1 X 1 0 0 0 X 0 X 0 0 X X^2+X 0 0 X X^2+X X^2 0 X^2+X X^2 X^2+X X^2 X X X^2+X X^2 X 0 X 0 X^2 0 X X X^2+X X 0 X X^2 X^2 X X X^2+X X 0 0 0 0 X X^2+X X X 0 X^2 X^2 X^2+X X X X X X^2+X X^2 X 0 X X^2 X^2 0 X^2+X X^2+X X^2+X X^2 0 0 X 0 X^2 X^2 X X 0 0 X X 0 X^2+X X 0 0 X^2+X X 0 X X^2 X X^2 0 X^2+X X X^2+X 0 X^2+X 0 0 X X^2 X X X^2 X X^2+X X^2 X^2 X 0 0 X X 0 0 X X^2+X X X^2+X X X^2 X^2 0 X^2 X^2+X X X^2+X X X^2+X X^2 0 0 X X X 0 X 0 X^2+X X^2+X 0 X^2 0 X X^2+X X^2 X^2+X X^2+X X^2 0 X^2 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 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 X^2 0 X^2 X^2 0 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 0 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 X^2 0 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 X^2 0 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 0 X^2 0 0 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 0 0 0 0 X^2 X^2 0 X^2 0 0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 X^2 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 0 X^2 0 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 0 0 X^2 0 0 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 X^2 0 0 0 0 0 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 0 0 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 0 X^2 0 X^2 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 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 0 X^2 0 X^2 X^2 0 0 0 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 0 0 0 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 0 0 0 0 0 0 0 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 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 0 X^2 0 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 0 0 X^2 0 X^2 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 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+207x^64+8x^65+312x^66+48x^67+790x^68+168x^69+850x^70+360x^71+1398x^72+624x^73+1606x^74+864x^75+1975x^76+816x^77+1668x^78+592x^79+1431x^80+392x^81+878x^82+176x^83+595x^84+40x^85+282x^86+8x^87+193x^88+34x^90+45x^92+17x^96+2x^98+3x^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 27.5 seconds.