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 1 X X^2 X X^2 0 0 X 1 X X 0 1 1 0 X^2 X X 0 1 1 1 1 0 X^2 0 1 1 1 1 0 1 1 1 0 1 X 0 X 1 X 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^2 0 0 X^2+X X X^2+X 0 0 0 X^2 0 X X^2 0 X^2+X 0 X^2 0 X^2+X X 0 X^2 X^2 X X^2+X X^2+X X 0 X^2+X 0 0 X^2+X X X X^2+X X X X^2 0 X X X^2 X^2+X X^2+X X^2+X X^2 0 X^2 0 X X 0 X^2 X^2+X X^2+X X 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 X X X X^2+X X^2 X^2 X X^2 X^2+X 0 X^2 X^2 X^2 0 X^2+X X^2+X X^2 X^2+X X 0 X 0 0 X 0 X^2+X X^2 X^2 X^2 0 0 X^2 X X X^2 X^2+X X^2 X 0 X X X^2 X X^2+X 0 X X X^2 X^2 X^2+X X^2 0 X^2 X X^2+X 0 X^2+X 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 0 0 X X^2+X 0 X X X 0 X^2 0 X^2+X X^2+X X^2+X X X X X^2+X 0 X^2 X X X^2 0 X X^2 X^2 X X X X X^2+X X^2+X X 0 X 0 X X^2+X X^2+X X 0 X^2 X^2 0 X 0 X^2 X^2 0 0 X X^2 X^2+X 0 0 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 X^2 0 0 0 0 0 0 X^2 0 X^2 0 X^2 X^2 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 0 X^2 0 0 0 X^2 0 X^2 0 0 0 X^2 0 0 0 X^2 0 X^2 0 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 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 0 0 0 0 0 0 X^2 0 X^2 0 X^2 0 0 X^2 0 X^2 0 X^2 X^2 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 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 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 0 0 X^2 X^2 0 0 X^2 0 0 0 0 X^2 0 0 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 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 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 0 X^2 0 0 0 0 X^2 X^2 0 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 0 0 0 X^2 0 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 0 X^2 0 X^2 X^2 0 X^2 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 generates a code of length 80 over Z2[X]/(X^3) who´s minimum homogenous weight is 68. Homogenous weight enumerator: w(x)=1x^0+179x^68+4x^69+448x^70+56x^71+649x^72+100x^73+1020x^74+360x^75+1362x^76+608x^77+1508x^78+888x^79+2002x^80+928x^81+1680x^82+632x^83+1304x^84+380x^85+844x^86+112x^87+613x^88+28x^89+320x^90+234x^92+64x^94+44x^96+4x^98+9x^100+2x^104+1x^112 The gray image is a linear code over GF(2) with n=320, k=14 and d=136. This code was found by Heurico 1.16 in 28 seconds.