The generator matrix 1 0 1 1 1 X^2+X 1 X^3+X^2 1 1 1 X^3+X 1 1 X^3 1 X^3+X^2+X 1 1 X^2 1 X 1 1 1 1 1 X^3+X^2 1 1 X^2+X 1 1 X^3+X^2+X 1 1 1 X^3 1 1 0 1 1 X 1 X^2 X 1 1 1 1 X^2 X^3+X^2+X 1 1 1 1 1 1 1 1 1 1 X 1 1 X^3+X^2 X 1 1 X^3+X 1 1 1 X 1 1 1 X X^3+X^2+X 1 1 1 1 X^2 X^3 1 0 1 X+1 X^3+X^2+X X^3+X^2+1 1 X 1 X^2+X+1 X^3 1 1 X^2 X+1 1 X^2+1 1 X^3+X^2 X^3+X^2+X+1 1 X^3+1 1 0 X^3+X^2 X^2+X X^3+X X+1 1 X^3+X X^2+1 1 X^2+X X^3+X+1 1 X^3+X^2+1 X^3+X^2+X X^3+1 1 X^3+X^2 X^2+X+1 1 X^2+X X+1 1 X^3+X^2 1 1 X^2+X 1 0 0 1 1 0 X^3+X X^3+X X^3+X X^2 X X^3+X 0 0 X^3 1 X^3+X^2+X X^3 1 X^2 X X^3+X^2 1 1 0 X^3+X X X^3+X+1 X^2+X X^3+X^2+1 X^3+X^2 1 X^3+X+1 0 X^2+X+1 X^3+1 X^3 X X^3 0 0 X^2 X^2 X^3+X^2 0 X^3+X^2 0 X^2 X^2 X^3+X^2 0 X^3+X^2 X^3 X^2 X^3 X^2 0 X^3 X^2 X^3 X^2 0 0 0 X^3 X^3 0 0 X^3 0 0 X^2 X^2 X^2 X^2 X^3 X^3+X^2 X^3+X^2 X^3+X^2 0 X^3+X^2 X^3 X^3+X^2 0 X^2 0 X^3+X^2 X^3+X^2 X^2 X^3+X^2 X^3 0 0 X^2 0 X^3 X^2 X^2 X^2 X^3 0 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^3 X^3 X^2 X^3 0 X^3+X^2 X^3+X^2 X^2 X^3+X^2 0 X^3 X^3 X^2 0 X^2 X^2 X^3+X^2 X^2 X^3+X^2 X^3+X^2 0 0 0 X^3 0 X^3 X^3 X^3 X^3 0 X^3 0 0 X^3 0 X^3 0 0 0 X^3 0 X^3 X^3 X^3 0 X^3 0 0 X^3 0 0 0 0 X^3 X^3 0 X^3 0 X^3 X^3 X^3 0 X^3 0 X^3 X^3 X^3 X^3 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 0 0 X^3 0 0 0 X^3 X^3 0 X^3 0 X^3 X^3 0 0 0 0 0 0 0 0 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 X^3 X^3 0 0 X^3 X^3 X^3 0 0 0 X^3 X^3 0 0 0 X^3 X^3 0 X^3 X^3 0 0 X^3 0 X^3 0 X^3 X^3 X^3 X^3 0 0 0 X^3 0 0 X^3 0 X^3 X^3 X^3 0 X^3 0 0 X^3 X^3 0 X^3 0 X^3 0 0 0 0 X^3 X^3 0 0 X^3 X^3 0 X^3 0 X^3 0 X^3 X^3 0 X^3 0 generates a code of length 87 over Z2[X]/(X^4) who´s minimum homogenous weight is 82. Homogenous weight enumerator: w(x)=1x^0+171x^82+392x^83+408x^84+488x^85+410x^86+564x^87+293x^88+528x^89+296x^90+256x^91+139x^92+72x^93+40x^94+4x^95+20x^96+5x^98+1x^100+4x^102+2x^110+2x^120 The gray image is a linear code over GF(2) with n=696, k=12 and d=328. This code was found by Heurico 1.16 in 1.06 seconds.