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 1 1 X 1 X 1 1 1 1 1 1 X X^2 1 0 1 X 1 0 1 0 1 1 1 X 1 1 X 1 1 X^2 X X^2 1 0 X 0 X 0 0 X X^2+X 0 X^2 X X^2+X 0 X^2+X X^2 X^2+X X 0 X^2 X X^2 X^2+X 0 X^2+X 0 X^2 X X X^2 0 X X 0 X^2 X X^2+X 0 X^2 0 0 X X X^2+X X^2+X X X^2 X X X^2+X X^2 0 X^2+X X X^2+X 0 X^2+X X^2+X X X^2 X X X^2+X X^2 0 X^2+X 0 X X^2+X X^2 X^2 X X X^2 X^2 0 0 X X 0 X^2+X X 0 X^2 X X 0 X^2 X^2+X X X^2 X 0 X^2+X 0 0 X^2 X^2+X X 0 X X X^2 0 X^2+X X^2+X X^2 0 X X 0 0 X^2+X X^2+X X^2 X X^2 X^2 X^2 X^2+X X^2+X 0 0 X^2+X X^2 X^2+X 0 X^2+X X X X^2 0 X^2+X X 0 X X^2+X 0 X^2 X^2 0 X^2 X^2+X 0 X X X^2+X X^2 X 0 0 0 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 0 X^2 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 0 X^2 0 X^2 0 0 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 0 0 X^2 0 0 0 0 0 X^2 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 0 X^2 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 X^2 X^2 0 0 0 X^2 0 X^2 0 0 X^2 0 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 0 0 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 X^2 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 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 X^2 0 X^2 X^2 X^2 X^2 0 X^2 generates a code of length 74 over Z2[X]/(X^3) who´s minimum homogenous weight is 66. Homogenous weight enumerator: w(x)=1x^0+49x^66+76x^67+95x^68+62x^69+188x^70+74x^71+292x^72+48x^73+342x^74+80x^75+283x^76+46x^77+141x^78+64x^79+66x^80+30x^81+26x^82+12x^83+26x^84+4x^85+19x^86+14x^87+5x^88+2x^89+2x^90+1x^122 The gray image is a linear code over GF(2) with n=296, k=11 and d=132. This code was found by Heurico 1.16 in 0.615 seconds.