The generator matrix 1 0 1 1 1 X^2+X 1 1 X^3+X^2 1 1 X^3+X 1 1 0 1 1 X^2+X 1 1 X^3+X^2 1 1 X^3+X 1 1 0 1 1 X^2+X 1 X^3+X^2 1 1 1 X^3+X 1 X^3 1 1 X^2 1 1 X^2+X 1 1 1 X^3+X 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 X^3+X^2+X X X^3+X^2 0 X^2+X X^3+X^2 X^3+X 0 X^2+X X^3 X^3+X^2+X X^3+X^2 X^2 X^3+X X 1 1 X^2 1 1 1 1 1 1 0 1 X+1 X^2+X X^2+1 1 X^3+X^2+X+1 X^3+X^2 1 X^3+X X^3+1 1 0 X+1 1 X^2+X X^2+1 1 X^3+X^2 X^3+X^2+X+1 1 X^3+X X^3+1 1 0 X+1 1 X^2+X X^2+1 1 X^3+X^2 1 X^3+X^2+X+1 X^3+X X^3+1 1 X^3 1 X+1 X^2+X 1 X^3+X^2+X+1 X^2+1 1 X^2 X^3+X X^3+1 1 X^3+X^2+X 0 X X^3+X^2 0 X^2+X X^3+X^2 X^3+X 0 X^2+X X^3+X^2 X^3+X X^3 X^3+X^2+X X^2 X 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X^3+X+1 X^2+X+1 X^3+X^2 X^3+X+1 X^3+1 X^3+X+1 X^2+1 X^3+X^2+1 X^3+X+1 0 0 X^3 0 0 0 0 X^3 X^3 X^3 X^3 X^3 0 0 0 X^3 X^3 X^3 X^3 X^3 X^3 0 0 0 0 0 0 0 0 0 X^3 X^3 X^3 X^3 X^3 X^3 0 0 0 X^3 X^3 X^3 0 0 X^3 0 X^3 X^3 X^3 X^3 0 0 X^3 0 0 X^3 X^3 0 0 0 X^3 X^3 0 X^3 X^3 X^3 0 0 X^3 X^3 0 0 X^3 0 X^3 X^3 0 0 0 X^3 X^3 X^3 X^3 X^3 0 X^3 X^3 0 0 0 0 0 X^3 0 X^3 X^3 X^3 X^3 0 X^3 0 0 0 X^3 0 0 X^3 X^3 X^3 0 X^3 X^3 0 X^3 0 0 0 X^3 X^3 0 0 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 0 0 0 0 0 0 X^3 X^3 0 X^3 0 X^3 0 0 X^3 X^3 0 0 X^3 0 X^3 X^3 0 X^3 0 0 X^3 0 X^3 X^3 0 0 0 X^3 X^3 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 X^3 X^3 0 X^3 0 X^3 0 0 X^3 0 X^3 0 X^3 X^3 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 0 0 0 0 0 0 0 X^3 0 0 X^3 X^3 0 X^3 0 X^3 X^3 0 X^3 0 X^3 0 0 0 0 0 X^3 X^3 X^3 0 X^3 X^3 X^3 0 X^3 X^3 0 0 0 X^3 0 X^3 X^3 X^3 0 X^3 X^3 0 generates a code of length 89 over Z2[X]/(X^4) who´s minimum homogenous weight is 85. Homogenous weight enumerator: w(x)=1x^0+304x^85+68x^86+104x^87+276x^88+616x^89+224x^90+72x^91+40x^92+296x^93+28x^94+16x^95+2x^112+1x^128 The gray image is a linear code over GF(2) with n=712, k=11 and d=340. This code was found by Heurico 1.16 in 0.593 seconds.