The generator matrix 1 0 0 1 1 1 0 X^3 1 1 X^3 X^2 1 1 1 1 X^3+X X^3+X 1 X^3+X^2+X 1 X^3+X X 1 X^3+X 1 1 X^3+X 1 1 1 1 X^2+X 1 1 X^3+X 1 1 1 X^2 1 1 X^3+X^2 X^3+X^2 1 X^3 X^3+X^2 1 X 1 1 0 1 X^3+X 1 1 X^2+X 1 1 X^3+X^2 1 1 1 X^2 1 1 1 1 X^3+X^2+X 1 1 1 X^3+X^2 1 X^3+X^2 1 1 X 0 X 1 X^3 1 X^3+X^2+X 1 1 X^3+X^2+X 1 1 0 1 0 0 X^2+1 X^2+1 1 X^3+X^2+X X^3 X^3+X^2+1 1 1 X^3+X^2 1 X^2+X X+1 1 X^2+X X 1 X^3+X^2+X+1 1 1 X^3+X^2+X+1 X^2 X+1 X 1 X^2 X+1 X^3+X^2+X X^3+X^2 1 X^3+1 1 X^3+X X^3+X^2+X+1 X^2+X+1 X^3+X 1 0 X^2+X 1 0 X^2+X 1 1 X^3+1 1 X^2+X+1 X^2+1 1 X^3+X^2+X+1 1 X^3+X^2 X^3+1 X^2 X^2+X+1 X^3+X^2+1 X^2 X+1 X^3 0 X^3+X^2+X X^2+X X^3+1 X^3+X X^3+X+1 1 1 X^3+X^2+X X^2+1 X^3+X^2+X X^3+X X^3 1 X^2+X+1 1 1 X X^3+X^2+1 X X^2+X+1 X X^3+X X^3+X+1 X^3+X^2+X X^3+X+1 0 0 0 1 X+1 X^3+X+1 X^3 X^3+X^2+X+1 1 X^3+X^2+X X^2+1 1 X^3+X X^3+X^2+1 X X^3+X+1 X^2 X^3+X^2+1 1 X X^2 X^2+X+1 X^3+X^2+X X+1 X^2+1 1 X^2+X X^2 X^3+X^2+X+1 X+1 X^3+X^2+X+1 X^2+1 X^3 1 X^3+1 X^2+X 1 1 0 X+1 X^3+X^2+X X X^3+X^2+X X^3+X^2+X+1 1 1 X^2 X^3+X^2+1 X^3+X^2+X+1 X^3+X^2+X X^2+X X^3+X X^3+X^2+X X+1 X^2 X^3+X^2+X+1 X^2+X+1 1 X^3+X X^3 1 X^3+X^2+X 1 X^3+1 1 X+1 X^2 0 X^3+1 X^2+X+1 X^3+X^2+1 X^2+X X^3+X^2+X 1 1 1 X^3 X^3+1 0 1 1 X^2 1 X^3+X+1 1 1 X^3+1 1 X^2+1 X^3 0 0 0 X^3 X^3 0 X^3 X^3 X^3 0 0 X^3 0 X^3 0 X^3 X^3 0 0 X^3 X^3 0 0 0 X^3 X^3 0 X^3 0 0 X^3 X^3 0 X^3 0 X^3 X^3 0 X^3 X^3 0 X^3 0 0 0 X^3 X^3 0 X^3 0 0 0 0 0 0 X^3 0 X^3 X^3 X^3 0 0 X^3 X^3 X^3 0 X^3 0 0 0 0 X^3 0 X^3 X^3 0 0 0 X^3 0 X^3 X^3 X^3 X^3 0 X^3 0 X^3 X^3 generates a code of length 89 over Z2[X]/(X^4) who´s minimum homogenous weight is 84. Homogenous weight enumerator: w(x)=1x^0+184x^84+804x^85+844x^86+1452x^87+739x^88+1116x^89+625x^90+830x^91+347x^92+488x^93+184x^94+248x^95+138x^96+88x^97+56x^98+22x^99+13x^100+8x^101+2x^102+1x^106+2x^108 The gray image is a linear code over GF(2) with n=712, k=13 and d=336. This code was found by Heurico 1.16 in 6.09 seconds.