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 1 X^2 1 X 1 1 0 X 0 X^2+X X^2 X^3+X^2+X X^3+X^2 X X^2 X^2+X X^3 X^3+X 0 X^2+X X^2 X 0 X^2+X X^3+X^2 X^3+X X^3 X^3+X^2+X X^2 X X^3 X^3+X^2+X X^2 X X^2 X X^3 X^3+X^2+X 0 X^2+X 0 X^2+X X^2 X X^3+X^2 X^3+X 0 X^2+X 0 X^2+X X^2 X X^2 X X^3+X^2 X^3+X X^3+X^2 X^3+X X^3+X^2 X^3+X X^2 X 0 X^3 X^2+X X^3+X^2+X X^3 X^3+X^2+X 0 X^2+X 0 X^3 X^3 0 X^2+X X^3+X^2+X X^3+X^2+X X^2+X X^3 X^3 X^2+X X^3+X^2+X X^2+X X^3 X^3 X X^3+X X^3+X X^2 X^3+X^2 X^3+X^2 X^3+X X^2+X X^3+X^2 X^3 0 0 X^3+X^2 0 X^2 X^2 0 X^2 X^3+X^2 0 X^2 0 0 X^3+X^2 0 X^3+X^2 X^3 X^3 X^3 X^3 X^2 X^2 X^3+X^2 X^3+X^2 X^3 X^3 X^3 X^3 X^2 X^2 X^3+X^2 X^3+X^2 0 0 X^3+X^2 X^3+X^2 X^2 X^3+X^2 X^3 0 0 0 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^3 0 X^3+X^2 X^3 0 X^2 X^2 X^3+X^2 0 X^3 X^3 X^2 X^3 X^2 X^3 X^3 X^2 X^2 X^3 X^3 X^2 X^2 X^3 X^3 X^2 X^2 0 X^3+X^2 X^3 X^3 X^2 0 X^3+X^2 X^2 X^3+X^2 X^2 X^3 0 X^3 X^2 0 X^2 X^2 0 0 0 X^3 0 0 X^3 X^3 X^3 X^3 X^3 0 X^3 0 0 X^3 X^3 X^3 X^3 0 0 0 0 X^3 0 X^3 0 0 X^3 X^3 X^3 0 0 0 0 X^3 X^3 0 X^3 X^3 X^3 0 X^3 X^3 0 0 0 X^3 X^3 X^3 0 0 0 0 X^3 X^3 X^3 0 0 X^3 0 0 X^3 X^3 0 X^3 X^3 0 X^3 0 X^3 0 0 0 0 X^3 X^3 0 0 0 0 X^3 X^3 0 0 X^3 0 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 0 0 X^3 0 X^3 X^3 0 0 X^3 X^3 0 0 X^3 X^3 0 X^3 0 X^3 0 X^3 0 X^3 0 0 X^3 0 X^3 0 X^3 0 X^3 X^3 X^3 0 0 0 X^3 X^3 0 0 X^3 X^3 0 X^3 0 0 X^3 X^3 X^3 0 0 X^3 X^3 X^3 X^3 X^3 0 0 0 0 0 X^3 0 0 X^3 0 X^3 X^3 0 X^3 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+67x^84+48x^85+117x^86+160x^87+273x^88+744x^89+245x^90+152x^91+133x^92+40x^93+50x^94+8x^95+6x^96+3x^98+1x^174 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 1.22 seconds.