The generator matrix 1 0 0 0 1 1 1 1 X^2+X 1 1 1 X^2+X X X^2 X^2+X X X^2+X X^2 1 X^2 1 1 1 1 1 1 X^2+X 0 1 X^2+X X 1 0 0 1 1 X^2+X 1 1 1 0 X 0 X^2 1 1 1 1 1 1 1 0 X^2 1 1 1 1 0 0 1 X 0 X^2+X 1 1 1 1 1 X^2 1 1 1 0 X X^2+X 1 1 X^2+X X^2 1 1 1 1 X^2 1 0 1 0 0 0 X^2 1 X^2+1 1 X^2 X^2+X+1 X+1 1 1 0 1 X^2 1 1 X^2+X 1 X 1 X^2+X+1 X^2+1 X 1 X 1 X^2+X X^2 X^2 X X^2+X 1 X^2+X X^2+1 1 X^2+1 X+1 0 X 1 1 X^2 1 X^2 X+1 X^2+1 1 0 X+1 1 1 X X+1 1 0 0 1 X^2+1 X^2 1 1 X^2+X X^2+X 0 X 0 X^2+X X 1 X^2 1 X 0 X 1 0 1 0 X^2+X 1 X^2+1 1 X^2+X 0 0 1 0 0 X^2+1 X^2 1 1 X+1 X^2+X+1 X^2 X+1 X 1 1 1 X^2+X X X^2+X 1 X^2 X^2 X^2+X X+1 X^2+1 X^2+1 1 X^2+1 1 X^2 1 X^2+1 1 X X^2 1 X^2 X^2 X X 1 X^2+X+1 X^2+X 1 0 X^2 X^2+1 X^2+X+1 X^2+X+1 X+1 0 X^2+X 1 X^2 X^2+1 X^2+1 X+1 1 X^2+X+1 X^2+X 1 1 X 0 X X^2+X X+1 X^2+1 1 X^2+X+1 X^2+X+1 X+1 X+1 1 1 1 X 0 X^2+X+1 X X^2+X+1 X X^2 1 X^2+X 0 0 0 1 1 1 X^2+1 X 1 0 X+1 0 X 1 X+1 X^2+X X^2+X+1 X^2+X X^2+X+1 X^2 X^2+1 X^2+1 X+1 0 X^2 0 X^2+1 X^2 X X^2+X+1 1 X+1 X^2+X X 1 0 1 X^2 0 X+1 X^2+X+1 X^2 1 0 X^2+1 X^2+X X^2+X 1 X^2 0 X^2+1 X^2+X+1 X^2+1 X^2+X X^2+X X+1 0 X+1 X^2+X+1 X^2+X+1 X^2 X^2+X X^2+X X+1 X^2+X+1 X^2 X^2+X+1 0 X^2+X X^2+1 X^2+1 X^2+X+1 X X^2+1 X^2 X 0 1 1 X^2+X X^2+1 0 X X^2 X+1 X^2 0 0 0 0 X 0 0 0 0 X X X X X X X X X^2+X 0 X^2+X X X^2 X^2+X X^2 X 0 X^2 X^2 X^2 X^2+X X X^2 X X^2+X X^2+X 0 X^2+X X^2 X^2 X^2 X^2+X X X^2+X X^2+X X^2+X X 0 X^2 0 X^2+X X^2 X^2+X X^2 0 X^2+X X X^2+X X X^2 X^2 X^2 X^2+X X X X X X X^2+X 0 0 0 X X^2+X X^2+X 0 X X^2+X 0 X^2 X^2 0 X X^2+X 0 X^2 X generates a code of length 86 over Z2[X]/(X^3) who´s minimum homogenous weight is 77. Homogenous weight enumerator: w(x)=1x^0+92x^77+427x^78+730x^79+801x^80+1048x^81+944x^82+1230x^83+1215x^84+1514x^85+1152x^86+1122x^87+1128x^88+1210x^89+802x^90+862x^91+644x^92+566x^93+345x^94+202x^95+156x^96+78x^97+38x^98+44x^99+19x^100+4x^101+4x^102+2x^104+2x^108+2x^111 The gray image is a linear code over GF(2) with n=344, k=14 and d=154. This code was found by Heurico 1.13 in 5.39 seconds.