The generator matrix 1 0 0 0 1 1 1 1 X^2+X 1 1 X^2 0 1 0 0 X X X^2 1 1 0 1 X 1 X^2+X 1 0 1 X 1 X 1 1 1 X X^2 X 1 1 1 1 1 0 X 1 1 1 1 1 X^2+X X^2+X 1 1 X^2 0 1 0 X^2 1 X 1 1 1 X^2 X^2 1 1 X^2+X X^2 1 1 1 1 0 1 X^2 1 1 X 1 1 1 0 1 0 0 0 X^2 1 X^2+1 1 X^2 X^2+X+1 1 X^2+X X^2+1 1 1 X 1 1 X^2 X^2+1 X^2 X^2+X+1 1 X X X 0 X+1 1 0 1 1 X^2+X+1 X^2+X X 0 X X+1 1 0 X^2+X 0 1 1 0 X^2+X+1 X^2+1 X+1 1 0 1 X^2+X X^2 X 1 X^2 X^2+X 0 X^2+X+1 1 X^2+X X^2 1 1 1 X^2+X X 0 1 X X^2 0 X^2+1 X^2+X X+1 1 X^2+X+1 X^2 1 0 X^2+X 0 0 0 1 0 0 X^2+1 X^2 1 1 X+1 X^2+X+1 1 1 X^2 0 X^2 1 X+1 X X X^2+X 1 X X^2+1 X+1 X^2 1 1 1 X+1 X^2 X X^2+1 X+1 1 1 1 X X^2+X X+1 X^2+X 0 X^2 X^2+X 0 X^2+1 0 X^2+1 X^2+X X 1 X^2 0 X+1 X^2 X 1 1 1 X 1 X^2+1 X^2+1 1 X+1 X^2+X+1 X^2+X+1 X 0 X^2 X^2+X X^2+1 X^2+X+1 0 1 X^2 X X^2+X X^2 X^2+X X^2+X 0 0 0 0 0 1 1 1 X^2+1 X 1 0 X+1 X^2+X X^2+1 X X+1 X 0 1 X+1 X^2+1 X^2+X+1 X^2+X+1 X 0 X 1 1 1 X X+1 X^2+X+1 X X+1 X X X^2+X+1 X^2+X 1 1 1 X X^2 X+1 X X^2+1 X^2+X X X^2+1 X^2 X^2 0 X+1 1 X^2+X 1 X 1 X^2+X 0 0 X^2+X+1 X+1 X^2+X X X^2+X+1 X^2+1 1 X^2+X+1 1 1 X^2+X X+1 X^2+X X+1 X^2+X 1 X^2+X+1 X+1 X^2 X^2 1 X 0 0 0 0 0 X 0 0 0 0 X X X X X X X^2 X^2 0 0 X^2 X X^2 0 0 X X^2+X X X^2 X^2+X X^2+X X^2+X X^2+X X^2 X^2 X^2 X X^2+X X X^2+X X X^2+X 0 0 X^2 0 0 X X^2 X^2 X X 0 X^2 X^2+X X^2+X X^2+X X^2 0 X^2+X X^2+X X^2 0 X^2 X X 0 X X^2+X 0 X^2 0 X X X^2 X^2+X X 0 X X^2 X^2 X^2 0 0 generates a code of length 83 over Z2[X]/(X^3) who´s minimum homogenous weight is 74. Homogenous weight enumerator: w(x)=1x^0+174x^74+310x^75+736x^76+710x^77+1153x^78+954x^79+1317x^80+1128x^81+1271x^82+1246x^83+1486x^84+984x^85+1151x^86+808x^87+964x^88+564x^89+566x^90+284x^91+246x^92+130x^93+85x^94+36x^95+46x^96+4x^97+13x^98+8x^99+4x^100+3x^102+2x^103 The gray image is a linear code over GF(2) with n=332, k=14 and d=148. This code was found by Heurico 1.13 in 5.19 seconds.