The generator matrix 1 0 0 1 1 1 X 1 X^2+X 1 1 0 1 X^2+X 1 1 1 X^2+X 1 X^2+X 0 0 1 X^2 1 X 1 1 1 1 X 0 0 1 X^2+X 1 1 1 X^2 1 X^2 X^2+X 1 X X^2 X 1 X^2+X 1 1 1 X^2 1 X 1 X^2 1 1 0 1 1 X^2+X X^2+X X^2+X X X^2+X 1 1 0 1 1 X^2+X 1 1 X^2+X X^2+X X 1 1 1 0 1 1 0 X^2+X 1 0 1 0 0 1 X^2+X+1 1 X^2 0 X^2 X+1 1 X^2+1 1 X^2 X+1 X^2 1 1 1 X^2+X 1 X 1 X^2+X+1 X^2+X X+1 X^2+X 0 X^2 1 1 X^2 X^2+1 1 X^2+X+1 X^2+1 X^2+X 1 X^2 X X^2 X+1 X 1 1 X^2+X X 0 0 1 1 X^2+1 1 1 1 X X X X^2+1 X^2+X+1 1 0 1 1 1 0 X^2 X^2+X X X^2+X+1 1 X^2+X X^2+X+1 1 X^2+X 1 X+1 0 X^2+X+1 X^2 X^2 1 1 1 X^2+X 0 0 1 1 X+1 0 1 X+1 1 X X^2+1 X^2+1 X^2 0 0 X^2+X+1 X+1 1 X X^2 1 X+1 0 X^2+X 1 1 0 X^2+X+1 X^2+X X+1 X+1 X^2 1 X+1 X+1 X X X^2+X 0 X^2+1 1 1 1 1 X X^2+X X^2 1 X^2+X X^2+X 1 X^2 0 X^2 X^2+1 X+1 1 X^2+1 1 0 X^2+X X^2+X+1 1 X^2+X X^2 X^2+1 0 X^2+1 1 X^2+X+1 X^2 1 X^2+1 X+1 X 1 X^2+X X+1 1 X^2+X+1 1 X^2+X X X X^2+1 X 0 0 0 X X X^2+X X^2 X^2+X 0 0 X 0 X 0 X X^2 0 X^2+X X^2 X^2+X X^2+X X^2+X X^2+X X^2+X X^2 0 0 X^2 X X^2 X X^2+X X X^2+X X X^2 X X^2+X X^2 X X X^2 X^2 X^2+X 0 X^2 0 X^2+X 0 0 0 X^2+X 0 X X 0 X^2 X^2 X^2+X X^2+X X^2+X X^2+X X X^2+X 0 0 X^2 X^2+X 0 0 X X X^2+X 0 X^2+X X^2 X^2+X X^2 X^2 0 X^2 X X^2 0 0 X^2+X 0 0 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 0 0 X^2 0 0 X^2 0 X^2 X^2 0 X^2 0 0 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 X^2 X^2 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 X^2 0 X^2 0 0 0 0 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 X^2 0 X^2 0 0 0 0 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 X^2 0 X^2 0 0 X^2 0 X^2 0 0 0 0 X^2 0 X^2 generates a code of length 86 over Z2[X]/(X^3) who´s minimum homogenous weight is 78. Homogenous weight enumerator: w(x)=1x^0+166x^78+240x^79+465x^80+520x^81+614x^82+712x^83+678x^84+732x^85+563x^86+584x^87+534x^88+600x^89+408x^90+332x^91+328x^92+204x^93+182x^94+112x^95+78x^96+56x^97+34x^98+4x^99+24x^100+15x^102+2x^104+2x^108+2x^110 The gray image is a linear code over GF(2) with n=344, k=13 and d=156. This code was found by Heurico 1.16 in 4.57 seconds.