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 0 1 1 1 X^2+X 1 0 1 1 X^2+X 1 1 0 1 1 1 X^2+X X^2+X 0 1 1 1 0 1 1 X^2 1 1 1 1 1 X^2+X 1 1 X^2+X 0 1 0 1 1 0 1 X^2 X 1 1 1 0 X 1 X 1 X^2 1 1 1 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 1 X+1 X^2+X X^2+1 1 0 1 X+1 X^2+1 1 X^2+X X^2+1 1 0 X+1 X^2+X 1 1 1 0 X^2+X X+1 1 X^2+1 X 1 X^2+1 0 X+1 X^2+X X^2+1 1 X^2+1 0 1 1 X 1 X^2 0 1 1 1 1 X^2+X 0 X^2 1 0 X^2+1 1 X^2+X+1 1 X+1 X^2+X X^2+X 0 0 0 0 0 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 X^2 X^2 0 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 0 0 X^2 0 0 0 X^2 0 0 0 0 0 X^2 0 0 X^2 X^2 0 X^2 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 X^2 0 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 X^2 X^2 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 X^2 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 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 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 0 0 X^2 X^2 0 0 X^2 X^2 0 0 X^2 0 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2 0 X^2 X^2 0 X^2 0 0 X^2 0 0 X^2 X^2 0 0 0 0 0 0 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 0 X^2 0 0 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 X^2 X^2 0 0 0 X^2 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 0 X^2 0 X^2 X^2 0 X^2 0 0 0 0 0 0 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 X^2 0 0 0 X^2 0 X^2 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 X^2 0 0 X^2 X^2 X^2 0 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 0 X^2 0 0 0 0 X^2 X^2 X^2 X^2 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 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 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 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 generates a code of length 78 over Z2[X]/(X^3) who´s minimum homogenous weight is 64. Homogenous weight enumerator: w(x)=1x^0+53x^64+8x^65+52x^66+44x^67+124x^68+172x^69+261x^70+436x^71+522x^72+776x^73+996x^74+1176x^75+1332x^76+1504x^77+1525x^78+1472x^79+1448x^80+1152x^81+930x^82+788x^83+480x^84+436x^85+214x^86+172x^87+98x^88+48x^89+64x^90+8x^91+28x^92+26x^94+6x^96+22x^98+4x^100+5x^102+1x^110 The gray image is a linear code over GF(2) with n=312, k=14 and d=128. This code was found by Heurico 1.16 in 19.2 seconds.