The generator matrix 1 0 1 1 1 X^2+X 1 X^3+X^2 1 1 1 X^3+X 1 1 X^3 1 X^3+X^2+X 1 1 X^2 1 X 1 1 1 1 1 X^3+X^2 1 1 X^2+X 1 1 X^3+X^2+X 1 0 1 X 1 1 1 1 X^3 X 1 1 1 1 X^2 1 1 1 1 1 1 1 1 1 1 1 1 1 X 0 1 1 1 1 1 X 1 1 1 X X 1 1 X^2 1 1 1 X^2 X^2 1 1 X^2 X 1 1 0 1 X+1 X^3+X^2+X X^3+X^2+1 1 X 1 X^2+X+1 X^3 1 1 X^2 X+1 1 X^2+1 1 X^3+X^2 X^3+X^2+X+1 1 X^3+1 1 0 X^3+X^2 X^2+X X^3+X X+1 1 X^3+X X^2+1 1 X^2+X X^3+X+1 1 X^3+1 1 X^2+X 1 X^3 1 X^3+X^2 X^3+X^2+X+1 1 1 X^3+X^2+1 X^3+X X^3+X^2 X^2+X+1 1 0 X^3+X^2+X X^2+X 0 0 X^3+X X^2 X X^3+X X^3+X X^3+X^2 0 X^3+X^2 0 1 X^2+X X+1 X^2+1 X^3+X^2 X^2+X 1 X^3+X^2+X X^2+X 0 X^3+X^2 X^2 X^3+X X^2+X+1 1 X^2+1 X^2+1 X^3+X^2+X+1 1 1 X^3+1 X^3 1 X^3+X^2 X^3+X X^2+1 0 0 X^2 X^2 X^3+X^2 0 X^3+X^2 0 X^2 X^2 X^3+X^2 0 X^3+X^2 X^3 X^2 X^3 X^2 0 X^3 X^2 X^3 X^2 0 0 0 X^3 X^3 0 0 X^3 0 0 X^2 X^2 X^3 0 X^3+X^2 X^3+X^2 X^3+X^2 X^2 0 X^3 X^2 0 X^3+X^2 X^2 X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^2 X^2 0 X^3 X^2 X^3+X^2 X^3+X^2 0 X^3+X^2 0 X^3 X^3 X^2 X^3 X^2 X^3+X^2 0 X^3 X^2 X^2 X^3+X^2 X^3+X^2 X^3 X^3 X^2 X^2 X^2 0 X^3 X^3+X^2 X^3 0 0 X^3 X^3 X^3+X^2 0 X^2 0 0 0 X^3 0 X^3 X^3 X^3 X^3 0 X^3 0 0 X^3 0 X^3 0 0 0 X^3 0 X^3 X^3 X^3 0 X^3 0 0 X^3 0 0 0 0 X^3 X^3 X^3 X^3 0 0 X^3 X^3 X^3 X^3 X^3 0 X^3 0 X^3 0 X^3 0 0 X^3 X^3 X^3 X^3 0 0 X^3 X^3 0 0 0 0 0 X^3 X^3 0 0 0 X^3 X^3 0 X^3 X^3 X^3 X^3 0 0 X^3 0 0 0 0 0 X^3 0 0 X^3 0 0 0 0 X^3 0 X^3 X^3 X^3 X^3 0 X^3 0 0 0 X^3 X^3 X^3 0 0 X^3 X^3 X^3 0 0 0 X^3 X^3 0 0 0 X^3 X^3 0 0 0 0 X^3 X^3 0 X^3 X^3 X^3 X^3 0 X^3 0 X^3 0 0 0 X^3 X^3 0 X^3 0 X^3 0 X^3 X^3 X^3 0 X^3 X^3 0 0 X^3 0 X^3 0 X^3 X^3 0 0 X^3 0 0 X^3 X^3 0 X^3 0 0 0 X^3 X^3 0 0 0 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+200x^84+264x^85+603x^86+292x^87+512x^88+488x^89+501x^90+264x^91+504x^92+186x^93+171x^94+20x^95+63x^96+14x^97+2x^98+4x^101+1x^102+2x^109+2x^113+1x^122+1x^126 The gray image is a linear code over GF(2) with n=712, k=12 and d=336. This code was found by Heurico 1.16 in 1.09 seconds.