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 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 X^3+X^2 X^3+X^2+X X 0 X^3+X^2 X^3 X X 0 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 X^3+X+1 X^3+X^2+1 X^2+X+1 1 X+1 X^2+1 X+1 X^2+1 X^3+X^2+X+1 X^3+1 X^3+X+1 X^3+X^2+1 X^3+X^2+X+1 X^2+X+1 X^3+1 1 1 1 1 1 1 1 X^2 1 1 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 0 0 X^3 X^3 0 0 X^3 X^3 0 X^3 0 X^3 X^3 0 X^3 0 X^3 0 X^3 X^3 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 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 0 0 0 0 X^3 X^3 X^3 X^3 0 X^3 X^3 X^3 X^3 0 0 0 X^3 0 0 X^3 X^3 X^3 X^3 X^3 X^3 0 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 X^3 0 X^3 0 X^3 0 0 X^3 0 X^3 X^3 0 0 0 X^3 X^3 0 0 0 0 X^3 X^3 X^3 0 X^3 0 generates a code of length 90 over Z2[X]/(X^4) who´s minimum homogenous weight is 86. Homogenous weight enumerator: w(x)=1x^0+314x^86+60x^87+144x^88+208x^89+662x^90+200x^91+80x^92+16x^93+302x^94+28x^95+30x^96+2x^114+1x^128 The gray image is a linear code over GF(2) with n=720, k=11 and d=344. This code was found by Heurico 1.16 in 0.594 seconds.