The generator matrix 1 0 0 0 1 1 1 X^2 1 1 X^2+X 1 1 X^3+X^2 X^2+X 1 1 1 0 X^3+X^2 1 X^2 X^3+X^2+X X X^3+X^2 1 1 X^3+X^2 1 X^3+X^2 X^3+X^2 1 X X^3+X X^3+X 1 1 1 1 X^2+X 1 1 1 1 X^2 1 1 1 X^3+X^2+X X^3 1 1 1 X^2 1 X^2+X 1 X^3+X 1 X^3 1 X^3+X X 1 1 X^3+X 1 0 1 0 0 0 X^3+1 X^3+1 1 X^3+X^2+X X^3+X X^3+X^2+X X+1 X^3+X^2+X+1 1 1 X^2+1 0 X^3 X X^2+X X^3+X^2+1 1 1 1 X^2 X^2+X+1 X^3+X^2+X 1 X^3 1 1 1 X^3 X^3 X^2 X^3+X^2+X+1 X^3+1 X+1 X X^3+X^2 X^3 X X^3+X^2+X+1 X^3+1 X X^2+1 X^3+X^2 X^2+X+1 1 X X^2+X 0 X^3+X X^2 0 1 X^2 1 X^3+X^2 X X^3 1 1 X^2+1 X^2 1 0 0 0 1 0 1 1 X^2 X^2+1 0 X^3+1 1 X^2+1 X^2+X X^3+X^2+X+1 X^3 X^2 1 X 1 1 1 X X^2+1 X^2+1 X^3+X 1 X^3+X^2+1 X X^3 X^3+X+1 X^2 X^3+X^2+X X^3+X^2 1 1 X^2+X X^3+X+1 X^3+1 X^3+X^2+X 1 X^3+X X^2+X X^2+X X^2+X+1 X X^3+X^2+X X^2+1 X^3+X X 1 X+1 1 X^3 1 X^2+X X^3+X^2 X^2+X+1 X^3+X^2+X+1 X^3+X+1 1 X^3+X^2+1 1 X^2 X X^2+1 X+1 0 0 0 0 1 1 X^2 X^2+1 1 X^2+X+1 X^3+X X^2+1 X^2+1 X^2+X X^3+X^2+X X^2+1 X^2+X+1 X^3+X^2+X+1 X^3+1 X^3+X^2+X+1 0 X^3+1 X+1 X^2+X+1 X^2+X 1 X^3+X X^3 X^2+X X X+1 X^2+X+1 0 1 X+1 X^3+X X^3+1 X^3+X^2 X^3+X+1 X^3+X^2+X X^3+X^2+1 X^3+X^2+X+1 X 0 X^3+X 1 X^2+X+1 X^3+X^2+X X^3+X+1 0 X^3+X X^2+1 X^2+1 X^3+X^2+X X^3+X X 1 X^3+X^2+1 0 X^3+X^2 X^3+X X^3+X^2+X X^2 X^2+X+1 X X^3+X^2 0 0 0 0 0 0 X^3+X^2 0 X^3+X^2 0 X^3 X^3 X^3 X^3 X^3 X^3 0 0 X^3 0 0 X^3 X^3 0 0 X^2 X^2 X^2 X^3+X^2 X^3+X^2 X^2 X^3+X^2 X^2 X^3+X^2 X^3 X^3+X^2 0 X^3+X^2 X^2 X^3+X^2 X^3+X^2 X^2 X^3+X^2 0 X^2 0 X^2 X^3 X^3+X^2 X^3 X^2 X^2 0 X^3 0 X^2 X^2 X^3+X^2 X^2 X^3 X^3+X^2 X^3 0 X^2 X^2 X^3 0 0 0 generates a code of length 67 over Z2[X]/(X^4) who´s minimum homogenous weight is 58. Homogenous weight enumerator: w(x)=1x^0+144x^58+836x^59+2165x^60+4832x^61+8693x^62+14378x^63+20151x^64+28658x^65+32355x^66+37358x^67+32913x^68+28588x^69+20674x^70+14716x^71+7926x^72+4186x^73+2077x^74+894x^75+320x^76+176x^77+55x^78+24x^79+8x^80+8x^81+2x^82+4x^84+2x^87 The gray image is a linear code over GF(2) with n=536, k=18 and d=232. This code was found by Heurico 1.16 in 561 seconds.