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 X^2 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^3+X^2 X^2+X+1 X^3+X+1 X^3+1 X^3+X+1 X^2+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 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 X^3 0 X^3 0 0 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 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 X^3 0 X^3 X^3 X^3 X^3 generates a code of length 87 over Z2[X]/(X^4) who´s minimum homogenous weight is 83. Homogenous weight enumerator: w(x)=1x^0+320x^83+66x^84+120x^85+192x^86+672x^87+214x^88+112x^89+288x^91+36x^92+24x^93+2x^108+1x^128 The gray image is a linear code over GF(2) with n=696, k=11 and d=332. This code was found by Heurico 1.16 in 0.531 seconds.