The generator matrix 1 0 0 0 1 1 1 1 X^2 1 X^2+X X 1 X^2 1 1 X 1 1 0 1 0 1 0 1 X^2 0 X^2 1 1 1 1 1 X X X^2+X X 1 1 1 X 1 X^2 1 X^2+X 1 1 X^2 1 1 X 1 X 1 1 X X^2+X X^2+X X^2 1 1 1 1 X^2 0 1 1 0 1 0 1 X^2+X X^2+X X^2+X X 0 X^2+X 1 1 0 1 0 0 0 X^2 1 X^2+1 1 X^2+X+1 X^2 1 0 1 X+1 X^2+1 1 X^2+X X^2+X+1 X X^2+1 1 X+1 1 0 X^2+X 1 1 X X^2+1 X^2+X 0 0 X^2+X 1 X^2 X^2+X 1 X^2+1 X^2+X+1 1 X^2+X+1 1 X^2 1 X X^2+X+1 X 0 X X X+1 1 0 0 1 1 1 X 1 X^2+1 X+1 X^2 X^2 0 0 X^2+X 1 1 X^2+X 1 X^2 X^2 1 X^2+X X^2 X^2 1 X^2 0 0 1 0 0 X^2+1 1 X^2+X X+1 X^2+1 1 X^2 X^2+X+1 X^2+1 X^2 0 X^2 X^2+1 X+1 1 X^2+1 X^2+1 X^2 X^2+X X^2+X 1 X^2+1 X+1 0 X^2 1 1 X^2 X^2 X 1 1 X^2+1 X 1 X^2+X+1 X^2+X X X 1 1 X^2+X X^2 X 0 1 X^2+X 0 X^2+X 1 X+1 0 X 1 X^2+1 X X^2 X 1 1 X^2 X+1 X^2+X X^2 0 X^2+1 X^2 1 X X^2 1 1 X+1 X^2 0 0 0 1 1 1 X^2 X+1 X+1 X^2+1 X^2+1 X^2+1 X X X^2 X^2+X+1 0 X^2+1 X^2+X+1 X^2+1 X^2 X^2 X 1 X^2+1 0 X^2+X+1 0 X^2+X X X+1 X^2 X^2+X 1 X^2 X^2+1 X^2+1 X X^2+1 X^2+X X^2+X X X X^2+X+1 X^2+X+1 X+1 1 1 X^2+X X^2+X+1 X^2+X+1 1 1 X^2+X+1 X^2+X X^2+X X^2+X+1 X X 1 X^2+1 X X^2 X^2 X^2 0 X X+1 X^2+X+1 1 1 1 X^2+X 0 1 X+1 X^2+X+1 X^2+X+1 0 0 0 0 0 X 0 0 0 0 X X X X^2+X X X X^2 X^2 0 0 X^2 X X^2 0 X^2+X 0 X^2+X X X^2 X X^2+X X^2+X X^2 X^2 X^2+X X X^2 0 X^2 X X X^2+X X^2 X^2+X 0 0 X 0 0 X^2+X X^2+X X^2 X^2+X X^2+X X 0 X^2 X^2+X X^2+X X^2 0 X^2+X X^2+X 0 X^2+X X X X^2+X 0 X X^2+X X 0 X^2 0 X^2 X^2+X X X 0 generates a code of length 79 over Z2[X]/(X^3) who´s minimum homogenous weight is 70. Homogenous weight enumerator: w(x)=1x^0+88x^70+316x^71+602x^72+884x^73+858x^74+1300x^75+1001x^76+1482x^77+1145x^78+1516x^79+1128x^80+1364x^81+910x^82+1142x^83+621x^84+694x^85+544x^86+376x^87+169x^88+110x^89+66x^90+20x^91+24x^92+8x^93+3x^94+4x^96+2x^97+2x^98+2x^99+2x^100 The gray image is a linear code over GF(2) with n=316, k=14 and d=140. This code was found by Heurico 1.13 in 4.83 seconds.