The generator matrix 1 0 1 1 1 X^2+X 1 1 0 1 1 X^2+X 0 1 1 X^2+X 1 1 1 X 1 0 1 1 1 X^2 1 X^2+X 1 1 1 0 1 X^2+X 1 1 X^2+X 0 1 1 1 1 1 X^2+X 0 X^2 1 0 1 1 1 0 1 1 1 X^2 1 1 1 1 1 X 1 X^2 1 1 1 X^2 1 1 1 1 0 1 1 0 1 1 1 X^2+X 1 1 1 1 X 1 1 1 1 X 1 1 0 1 X+1 X^2+X 1 1 0 X+1 1 X^2+X X^2+1 1 1 0 X^2+1 1 X^2+X X+1 X^2+X+1 1 0 1 X^2+X X^2+1 X^2+1 1 0 1 X^2+X X+1 X^2 1 X^2+1 1 X^2+X X+1 1 1 X+1 X^2+X 0 X+1 X^2+X 1 1 1 0 1 X+1 X X^2+1 1 X^2+1 0 0 1 X^2+X X^2 X X^2+1 X^2+X+1 1 1 1 X X+1 X^2+X 1 X^2+X+1 0 1 X^2+1 1 X^2 0 1 1 X^2+X+1 X^2 1 1 X+1 1 X^2+1 1 0 X X+1 0 X^2+X X+1 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 0 0 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 X^2 X^2 0 X^2 X^2 0 0 0 0 X^2 0 X^2 X^2 X^2 0 0 X^2 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 0 0 0 0 0 0 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 0 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 X^2 0 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 0 0 X^2 0 X^2 0 0 0 X^2 0 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 0 0 0 0 0 X^2 0 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 0 X^2 0 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 0 0 0 0 X^2 0 X^2 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 0 0 0 0 0 0 X^2 0 0 X^2 X^2 0 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 0 X^2 X^2 X^2 0 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 0 0 0 X^2 0 0 X^2 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 X^2 0 0 X^2 0 0 X^2 X^2 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0 X^2 0 0 0 0 0 0 X^2 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 0 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 0 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 0 0 0 0 X^2 0 0 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 0 0 X^2 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 generates a code of length 92 over Z2[X]/(X^3) who´s minimum homogenous weight is 80. Homogenous weight enumerator: w(x)=1x^0+20x^80+34x^81+82x^82+90x^83+169x^84+230x^85+374x^86+450x^87+535x^88+594x^89+616x^90+644x^91+605x^92+652x^93+583x^94+612x^95+503x^96+438x^97+328x^98+226x^99+172x^100+94x^101+36x^102+26x^103+18x^104+6x^105+9x^106+13x^108+11x^110+9x^112+4x^114+1x^116+4x^118+1x^120+1x^122+1x^128 The gray image is a linear code over GF(2) with n=368, k=13 and d=160. This code was found by Heurico 1.16 in 6.72 seconds.