The generator matrix 1 0 0 0 0 1 1 1 0 1 X^2 1 X^2 1 X^2+X 1 0 1 1 X 1 1 X 1 0 0 1 1 1 1 X^2+X X^2 1 X^2+X 1 1 1 X 1 X^2+X X^2 X^2 0 X^2+X X 1 1 1 1 X^2+X 1 X 1 1 1 1 1 0 1 X^2 X^2 1 X X X X X^2+X 1 1 X^2+X X 0 1 1 0 X^2+X 1 0 1 0 0 0 0 0 X^2 X^2 1 1 1 1 1 1 X+1 X^2+X X^2+X+1 X^2+X X X^2 X^2+X+1 1 X^2+1 1 1 X^2 X X^2+X+1 X^2+X+1 0 1 X X^2+X 0 X^2+1 X^2+X+1 1 X X^2 X 1 1 X 1 X^2+X X^2+X 1 X^2+X 1 1 X^2+X X X+1 X^2+X+1 X^2+1 X^2+X+1 X X+1 1 1 1 1 1 X^2+X X^2 X^2+X X^2 X^2+1 X 1 X^2 X^2+X X^2+X 0 1 0 0 0 1 0 0 X^2 1 X^2+1 1 0 1 X+1 X^2+X+1 X^2+1 0 X 1 X X^2+X+1 1 1 0 X X^2+1 X^2+X+1 1 X X^2+X 0 X^2+X+1 X^2 0 1 1 X^2+X X^2+X+1 1 X^2+X 0 X^2 1 X^2+X+1 X^2+X X X X+1 X+1 X+1 X X X^2+X X^2 X^2 X X^2+1 X X+1 X 1 X^2+1 X^2+X+1 X^2 X+1 1 1 X^2+X 1 X+1 1 X X^2+1 X^2+X X+1 X^2+1 X 0 0 0 0 0 1 0 X^2+1 1 0 1 X^2 X^2+1 X+1 X^2 X^2+X X^2+1 X^2+X+1 X^2+X 1 0 X^2+X+1 X+1 X^2 X+1 X^2+1 0 X+1 1 X^2+X X^2+X X^2 1 X X^2+X 0 X^2+X+1 X+1 0 X^2+X 1 1 X+1 X^2+1 X^2+X+1 X^2+X X^2+X+1 X^2 X^2+1 0 0 X^2+X+1 1 1 X X X+1 X^2+1 0 X X^2+X+1 0 X^2+X+1 X^2+X X^2 1 X X 1 X^2+1 X+1 1 1 1 X+1 0 1 X+1 X^2 0 0 0 0 1 1 X^2 1 1 X^2+1 X^2 1 X+1 0 1 0 X^2+1 X+1 X^2+X X^2+X X^2+X+1 X^2+X 0 X^2+X X X+1 X 1 X^2+1 1 X+1 1 X^2+X+1 X^2+X+1 X X^2 0 X^2+X X+1 1 1 0 X^2+X 1 X 0 X^2+X+1 X+1 X^2 X+1 X^2+1 X X+1 X^2 X^2+1 X^2 X^2 1 X^2+X+1 X 0 X^2 X X^2+X+1 X^2 1 X^2+1 X^2+X+1 X X^2 0 0 X X^2+1 X+1 X+1 0 generates a code of length 77 over Z2[X]/(X^3) who´s minimum homogenous weight is 67. Homogenous weight enumerator: w(x)=1x^0+56x^67+384x^68+842x^69+1076x^70+1450x^71+1567x^72+2122x^73+2284x^74+2554x^75+2684x^76+2936x^77+2774x^78+2578x^79+2176x^80+2118x^81+1489x^82+1338x^83+860x^84+626x^85+406x^86+212x^87+126x^88+44x^89+33x^90+20x^91+8x^92+2x^94+2x^100 The gray image is a linear code over GF(2) with n=308, k=15 and d=134. This code was found by Heurico 1.13 in 16.2 seconds.