The generator matrix 1 0 0 1 1 1 X 1 X^2+X 1 1 X 1 X^2+X 1 X^2+X 1 1 0 0 1 1 X^2 1 1 0 X^2 1 1 1 1 X^2+X 1 X^2 0 X^2+X X^2 1 1 1 0 X^2 X 1 1 1 X 1 X 1 X^2+X 0 1 X^2 1 1 1 X^2+X 1 1 1 1 0 1 0 X^2+X 1 1 1 1 X^2 X^2 1 1 0 1 0 0 1 X^2+X+1 1 X^2 0 X^2 X^2+X+1 1 X+1 1 0 1 X^2 X^2+X 1 1 X^2+X+1 X^2+X+1 X 1 X^2+X 1 X 1 X^2+1 X^2+1 X^2+X+1 1 X^2 1 1 X^2 0 X 0 X+1 1 1 1 X X^2+X+1 X^2+X+1 1 X+1 1 X^2+1 1 1 1 0 X^2+1 X 0 1 X X+1 1 X 1 X^2 1 1 X^2+1 X^2+X 0 X^2+X X X^2 X^2+1 X 0 0 1 1 X+1 0 1 X+1 1 X X+1 X X X+1 X+1 X^2+1 X X^2+X+1 0 1 X^2+1 X^2 1 X^2 X^2+X X 1 X^2+X 1 X^2+1 X^2+X X^2+X+1 0 X^2 X+1 1 1 X^2+X+1 X^2 1 X^2+X 1 X X^2+X+1 X+1 X^2 0 1 X^2+1 X+1 0 X^2+X+1 X^2 1 X^2+1 0 0 X X^2 X^2+1 1 X^2+X+1 X+1 X X+1 X^2+X X^2 X X^2 X^2+1 1 X^2 X^2+1 X^2+1 0 0 0 X X X^2+X X^2 X^2+X 0 0 X X^2 X 0 X^2 X^2+X X X^2 X^2+X X 0 X^2 X 0 X^2+X X^2+X X^2 X X X^2 X^2 X X X X^2 X X X^2+X X^2 X^2 X^2+X X^2 X^2+X 0 X 0 X^2+X 0 X^2 X^2 0 X X^2 X X^2 X X^2 0 X^2 0 X^2+X 0 X^2 0 X X^2 X X^2 X 0 0 X X^2+X X^2 0 0 0 0 X^2 0 0 X^2 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 0 0 X^2 0 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 0 0 0 X^2 0 X^2 X^2 0 X^2 0 0 0 0 0 0 X^2 X^2 0 0 0 0 0 X^2 X^2 0 0 0 0 0 X^2 X^2 0 X^2 0 0 0 X^2 0 X^2 0 X^2 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 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+114x^66+208x^67+492x^68+430x^69+654x^70+630x^71+751x^72+614x^73+728x^74+586x^75+747x^76+514x^77+500x^78+294x^79+382x^80+206x^81+146x^82+68x^83+43x^84+20x^85+32x^86+2x^87+10x^88+4x^89+2x^91+6x^92+4x^93+2x^94+2x^95 The gray image is a linear code over GF(2) with n=296, k=13 and d=132. This code was found by Heurico 1.16 in 3.69 seconds.