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 1 1 X^2+X 1 1 1 1 0 0 1 X^2 1 X 1 1 X X^2 1 X 1 1 1 1 1 X 1 X 1 1 1 1 X^2+X 1 0 X^2 1 0 1 1 X^2+X X^2+X 1 1 1 1 1 0 X^2+X 1 1 1 1 0 1 0 X^2+X 1 0 1 X X^2 X^2 0 1 1 0 0 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 X 1 1 1 X^2+X X^2 X^2 X^2+X+1 1 1 X 0 X^2+X 0 1 X^2+1 1 X X 1 X^2+X+1 1 0 X^2+X+1 X^2+1 X X+1 1 X+1 X+1 X+1 X^2 X^2+X X^2+X X^2 1 X^2+1 X^2 X^2+X 0 X^2 1 X^2+X X 0 X^2+X X 1 1 X^2+X X^2 X 1 0 X^2+X+1 X^2+X 1 1 1 X^2+1 1 0 1 1 X^2+X+1 X^2+X X 1 1 X^2 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 1 0 0 0 X^2 X^2+X+1 0 1 X 1 X+1 X^2 X 1 X+1 X^2+X 1 X^2 X 0 X^2+1 X 1 X X^2+X+1 X^2 X^2+1 X^2+X X^2+1 X^2 X^2+1 X^2+X 1 X^2+X X^2+X X+1 0 1 X^2+1 X+1 1 X^2+X+1 X^2 X^2+1 1 1 X^2+X+1 X^2+X 0 0 1 X^2+X X^2+X+1 X X 1 X X^2+X X^2+1 X^2 X^2+1 1 X 1 X X X X^2 X^2+X+1 0 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 0 X+1 X^2 X^2 X^2 X^2+X+1 X^2+1 X+1 1 X^2+1 0 1 X^2 X+1 X^2+X X+1 X 1 X^2+1 X^2+X 0 0 X^2+X+1 1 X^2+X+1 1 X X+1 X+1 0 1 X^2+X X^2 X^2+X+1 1 0 X^2+X+1 X^2+X X^2+1 X^2+X+1 X+1 1 1 0 X^2+1 X 1 0 X^2+1 X^2+1 X X X^2+X+1 1 X^2+X+1 X+1 X+1 X^2+X+1 X^2 X^2+1 0 1 X X^2 X+1 0 1 X X+1 X^2+X 0 0 0 0 X 0 0 0 0 X X X X X X X X 0 X^2 X^2+X X^2 0 X^2+X X^2 X^2 0 X X^2 X X 0 X X X^2 X^2+X X^2+X X^2+X X^2 0 X^2 X^2 X^2 X^2+X 0 0 X^2+X 0 X^2 X^2+X X^2+X X^2+X 0 0 X X X^2+X 0 X^2+X X^2 X^2 X^2+X X^2 X^2 X X^2+X X^2 0 X^2 X^2+X X^2+X X^2 X 0 X X^2 X^2+X X X X^2 X 0 0 X X^2 X^2+X X^2+X X^2 generates a code of length 87 over Z2[X]/(X^3) who´s minimum homogenous weight is 78. Homogenous weight enumerator: w(x)=1x^0+170x^78+430x^79+568x^80+856x^81+1015x^82+1118x^83+1243x^84+1134x^85+1200x^86+1346x^87+1239x^88+1162x^89+1154x^90+906x^91+726x^92+654x^93+494x^94+334x^95+256x^96+182x^97+86x^98+36x^99+29x^100+24x^101+6x^102+6x^103+2x^104+3x^106+4x^109 The gray image is a linear code over GF(2) with n=348, k=14 and d=156. This code was found by Heurico 1.13 in 5.55 seconds.