The generator matrix 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X^2 X^2 X 1 1 1 0 X^3+X^2 0 0 0 X^2 X^3+X^2 X^2 0 0 0 0 X^2 X^3+X^2 X^2 X^3+X^2 0 0 X^2 X^2 X^3 X^3 X^3+X^2 X^2 0 X^3 0 X^2 X^3+X^2 X^2 X^2 X^3 X^3 0 X^3 X^3+X^2 X^3+X^2 X^2 X^3 X^3+X^2 X^2 X^3 X^2 0 X^3+X^2 0 X^3 X^3+X^2 X^3+X^2 0 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^3 X^3 X^3+X^2 0 X^3 X^3+X^2 0 X^3 X^3+X^2 0 X^2 X^2 0 X^2 X^2 X^3+X^2 X^3 X^3+X^2 X^3 X^2 0 X^2 0 X^3+X^2 0 X^3 X^2 X^3 0 X^2 X^3 X^3+X^2 X^2 X^2 X^2 0 0 X^3+X^2 0 X^2 X^2 X^3+X^2 0 X^2 0 0 X^3+X^2 X^2 X^3+X^2 0 0 0 X^2 X^2 0 0 X^2 X^3 X^3+X^2 X^3+X^2 X^3 X^3 X^2 0 X^3+X^2 X^3 X^3+X^2 0 X^2 X^3 X^3 X^2 0 X^2 X^2 X^2 X^3 X^3+X^2 0 X^3 X^3+X^2 X^3+X^2 X^3 X^2 X^3+X^2 0 X^3+X^2 X^2 X^3 0 X^3+X^2 X^3 X^2 X^2 0 X^3 X^3 X^2 X^3 0 0 X^3+X^2 X^2 X^3 X^2 X^2 X^3+X^2 X^3+X^2 X^3+X^2 0 X^3 X^2 X^3 X^3 0 X^3 X^3 X^2 X^3 X^2 X^3+X^2 X^2 0 X^3 0 0 0 X^3+X^2 X^2 0 X^3+X^2 X^2 X^2 0 X^3+X^2 0 0 X^3+X^2 X^2 0 X^3 X^3+X^2 X^3 X^3+X^2 X^2 0 0 X^3+X^2 X^3+X^2 X^2 X^3 X^3+X^2 X^2 X^3 X^3 X^3 X^3 0 X^3+X^2 X^3+X^2 X^3+X^2 0 X^3+X^2 0 X^3+X^2 X^3 0 X^2 X^3+X^2 X^2 0 X^3 X^2 X^3 X^3 0 X^3 X^3 X^3+X^2 X^2 0 X^3+X^2 X^3 X^2 0 X^3+X^2 X^3+X^2 X^2 X^3+X^2 X^3 X^3 X^2 X^3+X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^3 0 X^3+X^2 0 X^3 X^2 X^3 X^3+X^2 X^2 X^3 0 0 0 0 0 X^3 0 0 0 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 0 0 0 0 X^3 0 X^3 0 0 X^3 X^3 X^3 X^3 0 X^3 X^3 0 0 0 0 0 X^3 X^3 0 X^3 0 X^3 X^3 0 0 0 X^3 0 0 X^3 X^3 0 X^3 X^3 X^3 X^3 0 0 0 0 X^3 0 X^3 X^3 X^3 X^3 0 0 0 X^3 0 X^3 X^3 0 0 0 X^3 0 0 0 X^3 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+152x^84+160x^87+398x^88+704x^89+256x^90+160x^91+151x^92+65x^96+1x^172 The gray image is a linear code over GF(2) with n=712, k=11 and d=336. This code was found by Heurico 1.16 in 1.38 seconds.