The generator matrix 1 0 0 1 1 1 X^2+X 1 X 1 1 1 0 X 0 X 0 1 1 1 1 1 1 1 1 0 X^2 X X^2 1 X^2+X 1 1 1 1 1 0 1 X 1 X^2 X^2 1 0 1 0 1 X^2 1 X 1 X 1 0 X^2 1 X^2+X 1 1 1 1 X 1 0 1 1 1 0 X X^2+X 1 1 1 1 X^2+X 1 X 0 X X^2 1 1 1 1 1 1 0 1 0 0 1 X+1 1 X^2+X 0 X+1 X^2+X 1 1 1 X^2+X 1 1 1 X^2+1 X^2 X^2+X X+1 X+1 0 X^2 1 1 X^2 X X^2+X+1 1 X+1 0 X^2+X+1 X^2 0 1 X^2+X+1 1 1 X^2 1 X 1 X^2+1 0 X 1 X^2+X X X^2+1 1 X 0 0 X^2+X+1 1 X 1 0 X^2+1 1 X^2+1 1 X^2+X+1 X^2+1 X X^2+X 1 1 X^2+1 X^2+X X 1 1 X^2 1 1 1 X^2 X X^2+1 X^2+1 1 X+1 X^2+X 0 0 1 1 1 0 1 1 1 X^2+1 0 X^2 1 X^2 1 X+1 X^2+X X X^2+X+1 X X+1 0 X^2+1 1 X^2+X X^2 X^2+X+1 1 1 1 X^2+X+1 X X+1 X 0 X^2+X 0 X+1 1 X+1 1 1 X^2+1 X 0 1 1 0 X^2+1 1 X^2+X X^2 0 1 1 X^2+X X^2+X+1 X^2 X^2+X 0 X^2 X X^2+X+1 X^2+X 1 X+1 X^2+X 1 1 X+1 X X^2+X 1 1 X^2 X X^2 X^2+1 X+1 1 X^2+X+1 0 X^2+1 X^2+X+1 X X+1 0 0 0 X 0 0 X^2 X^2 X^2 X^2+X X X X^2+X X X 0 0 X^2 X^2+X X^2+X X X^2+X 0 0 0 X^2+X X X 0 X^2+X X^2+X X^2 X^2 X 0 X^2+X X^2 X^2+X X^2 0 X X^2 X^2+X X^2+X X X^2+X X X^2+X 0 X X^2 0 0 X^2 0 X^2+X X X^2 X X^2+X X^2 X^2+X X^2 0 X^2 X X 0 0 X^2 X 0 X^2 X^2+X 0 X 0 X X^2+X X^2+X X X X^2 X X^2 X 0 0 0 0 X X^2 X X^2+X X^2+X X^2 X X^2+X 0 X 0 X X^2 0 X^2 X^2+X 0 X^2+X X X^2+X 0 X X^2 X^2 X 0 0 X X^2 X^2 X 0 X X^2+X 0 0 X^2+X 0 X^2+X X^2 0 X^2+X X^2+X 0 X^2 X^2 X^2+X X^2+X X X X^2 X^2 0 X^2 0 X^2 X X^2+X X^2+X X X^2 X^2+X X^2 0 0 X^2+X X X X X X X X^2 X^2 X^2 X X^2 X^2 X^2 0 X^2 X^2+X 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+113x^78+300x^79+500x^80+494x^81+619x^82+770x^83+625x^84+606x^85+643x^86+578x^87+540x^88+610x^89+443x^90+364x^91+253x^92+198x^93+201x^94+86x^95+115x^96+56x^97+24x^98+22x^99+8x^100+4x^101+5x^102+8x^103+6x^104 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 4.66 seconds.