The generator matrix 1 0 0 0 1 1 1 1 X^3 1 X^3+X X 1 1 X^2+X 1 1 1 1 1 X^3+X 0 1 1 1 0 X X^3+X^2+X 1 X X^2 1 1 X^2+X X^3 0 X^3+X^2 X 1 X^3 X^2 1 1 X^2+X 1 X^3+X^2 1 X^3+X^2+X 1 0 1 X X^2+X X^3+X^2 X^2+X 1 1 1 X^2+X X 1 X^3+X^2 X X^3+X^2 1 1 0 1 0 0 X X^2+1 X^2+X X^3+X^2+X+1 1 X^3+X X^3+X^2 1 1 X^3+X+1 1 X^3+X^2+X X^3+1 X^2 X^2 X^3+X^2+X+1 X^3+X 1 X^3+X+1 1 X^2+X 1 X^3+X^2 1 X^3+X^2+X+1 X^2+X 1 X^3 X^3+1 0 1 1 1 1 X^3+X^2+X+1 X^2+X X^3 X^3+X X^3+X^2+X 1 X^3+X^2+1 X^2+X X X^3 X^3+X+1 X^3+X X^3+X^2 1 X^2+X 1 X^3 X^2+1 X^3 0 1 X^3+X^2 X^3+X^2+X+1 1 1 X^3 X^2+X+1 0 0 0 1 0 0 X^3 X^3+X+1 X+1 X^3+X+1 1 1 X^2+X+1 X^2+1 X^2 X^3+X^2 X^3+X X^3+X^2+X X^2+X+1 1 X^3+X^2+1 X^2 X^3+1 X X^3+X+1 0 X^3+X 1 X^3+X+1 X^3+X^2+X 1 X^3+X+1 X^2+X+1 X^3+X^2+X+1 X^3 X^3 X^3+X^2+X X^3+1 X^2 X^2+X+1 1 1 X+1 X^3+X X^3+X^2+1 X+1 X^3+X^2+X X^3+X^2 X^3+X^2+X X^3+X^2 1 X^3+X^2 X^2+X 1 X+1 1 X^3+X^2+X X^3+X^2+X+1 X^3+X^2+X+1 0 1 X^2+1 X^2 X^3+X 0 X^2+X 0 0 0 0 1 1 X^3+X+1 X^2+X+1 X^2+1 X X^3+X^2+X X^3+X^2+X+1 X+1 X^3+X^2 X^2+X 1 X^3 X^3+X X^3 X^3+1 X^3+1 1 X+1 X^3+X+1 X^3+X^2 X^2+X+1 X^3+X^2+1 X^2 X^2+1 X X 0 X^2+X X^2+1 1 X^3+X X^3+X+1 X^2 X^3 X^3 X^3+X^2+X+1 X^3+1 1 X^3+X+1 X^3+X^2+1 X+1 1 X^3+X^2+X 1 1 X^2 X^3+X X^3+1 0 X^3+X^2+X+1 X^3+1 X^3 X^2+X X^3+X^2+1 X^3+X+1 X^3+X X^2+X+1 X^3+X^2+X X^3+X^2 1 X^3+X+1 0 0 0 0 0 X^3 X^3 X^3 X^3 0 X^3 0 0 X^3 X^3 0 X^3 X^3 X^3 X^3 X^3 0 0 X^3 0 0 X^3 X^3 X^3 0 X^3 X^3 0 0 X^3 X^3 0 X^3 X^3 0 X^3 0 0 0 X^3 0 0 0 X^3 0 X^3 X^3 0 X^3 0 0 0 X^3 0 0 0 0 0 X^3 X^3 0 0 generates a code of length 66 over Z2[X]/(X^4) who´s minimum homogenous weight is 58. Homogenous weight enumerator: w(x)=1x^0+105x^58+1052x^59+2362x^60+4896x^61+7200x^62+10556x^63+14088x^64+15660x^65+18537x^66+16804x^67+14447x^68+10432x^69+6991x^70+4388x^71+1821x^72+1020x^73+392x^74+192x^75+77x^76+24x^77+17x^78+2x^80+6x^82+2x^84 The gray image is a linear code over GF(2) with n=528, k=17 and d=232. This code was found by Heurico 1.16 in 141 seconds.