The generator matrix 1 0 0 0 1 1 1 X 1 X 1 1 1 X X^2 1 0 1 X 1 1 1 1 1 X^2+X X^2+X X^2 X X^2+X X^2 1 1 X 0 0 1 X^2 1 1 1 1 0 1 1 X^2+X 0 0 X^2 X 0 1 1 1 X 1 X^2+X 1 1 1 1 1 1 0 1 X 1 X X^2 1 X^2+X X^2 0 X 1 1 X^2+X 1 X^2 X^2 1 X^2 1 X^2 0 1 0 1 0 0 X 0 X X X^2+X+1 1 X^2+X+1 1 X^2+X+1 1 1 X^2+X 0 X X^2 X^2+1 X^2 1 X^2 X^2+X+1 X X^2+X 1 1 1 1 X^2+X+1 X^2+1 1 1 X 0 0 X^2+X 1 X 1 X^2 1 X+1 1 X^2+X 1 X^2 X^2+X 1 X 1 X^2 1 1 1 X X^2+X X^2+1 X 1 X+1 X^2+X X^2+X+1 X^2+X 0 X^2 1 0 X^2+X 1 X^2 X^2 X X X^2+X X^2+X+1 X 1 X^2+X 1 X^2+X 1 1 X^2+X 0 0 1 0 X 1 X+1 1 X^2+X+1 X+1 X X^2+1 X^2 0 X+1 1 1 X^2+X+1 1 X^2+X+1 0 X X^2+X X^2 0 1 X X^2+X+1 X^2+X X^2+1 X^2+X+1 0 X^2 X^2+1 1 X^2+1 0 0 1 X^2+X+1 X+1 1 X^2+1 X^2 X^2 1 1 1 1 0 X^2+1 X^2+X X+1 X 1 X^2+X+1 X^2+X X^2+1 X^2 X 0 X^2+X+1 0 X^2+X+1 1 X 1 0 X^2+X 1 X 1 X^2 X+1 0 1 X^2+X 1 X^2+1 X^2+X X X^2 X^2+X+1 X X+1 0 0 0 1 X+1 1 X X+1 X^2+1 X^2+X X^2+1 0 X X+1 1 X^2+X+1 X 0 1 X^2+X X X^2+X X^2+X+1 X^2+1 1 0 X X+1 1 X 1 X^2+X+1 X^2+1 X^2 X^2+1 X^2+X 1 X^2+X+1 X^2+X 1 X^2+1 1 1 0 X^2 X 1 X^2+X 1 X^2+1 1 X^2 X^2+X+1 0 X^2 X X^2+X 1 0 X^2+X+1 X^2+X+1 X^2+X+1 1 1 X X^2+1 X+1 0 X^2 X X^2+X X^2+1 1 X^2+1 X^2+1 X^2+1 X+1 X^2 X^2 0 0 X+1 X^2+1 X^2+1 X 0 0 0 0 X^2 0 0 0 0 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 0 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 0 0 X^2 0 X^2 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 0 X^2 0 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 X^2 0 0 X^2 0 0 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 0 0 0 X^2 0 X^2 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 0 0 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 0 X^2 0 X^2 X^2 0 0 0 X^2 0 0 X^2 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 0 0 X^2 0 X^2 0 X^2 X^2 generates a code of length 85 over Z2[X]/(X^3) who´s minimum homogenous weight is 75. Homogenous weight enumerator: w(x)=1x^0+244x^75+460x^76+836x^77+1017x^78+1592x^79+1603x^80+2352x^81+1896x^82+2832x^83+2279x^84+2884x^85+2172x^86+2914x^87+2024x^88+2170x^89+1452x^90+1454x^91+848x^92+746x^93+387x^94+266x^95+124x^96+86x^97+42x^98+30x^99+21x^100+14x^101+8x^102+12x^103+2x^106 The gray image is a linear code over GF(2) with n=340, k=15 and d=150. This code was found by Heurico 1.16 in 74.6 seconds.