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 1 X^2 1 1 X 1 1 0 1 X^2+X 1 1 0 1 1 X^2+X 1 1 X 1 1 X^2 1 1 X^2 1 1 X 1 X X 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X^3 X^3+X 1 X^3+X 1 X^3+X^2 1 X^3+X^2+X 1 1 1 1 X^3 X^3+X 1 1 1 0 1 X+1 X^2+X X^2+1 1 X^3+1 1 X^3+X^2 X+1 X^3+X 1 X^3+X^2+X+1 X^3 1 X^3+X^2+X 1 X^3+X^2+1 X^2+X+1 X^2 1 X 1 1 0 X+1 1 X^2+X 1 X^3+X^2+X+1 X^3+X^2+1 1 0 X 1 X^3+X+1 1 1 X^2 X^2+X 1 X^3+X^2+X+1 X^2 1 X^2+1 X 1 X^3+1 X X X^2+1 X^2+X+1 X^2+1 X^3+X^2+X+1 1 X^3+X+1 X^3+1 X^3+X^2+X+1 1 X^2+X+1 X^3+X^2+X+1 X^2+1 X^3+1 X+1 1 X^3+X^2+X+1 X^2+1 X+1 X^3+1 X^3+X^2+X+1 0 1 1 X^2+X 1 1 1 X^2+X+1 1 X^2+X X^3+X^2 X^2+1 X^3+X+1 X^2 1 X^3+X^2 X^3+X^2+X+1 X^3+X+1 0 0 X^2 0 0 X^3 0 X^3 X^3 X^3 X^3 0 X^3 X^2 X^3+X^2 X^3+X^2 X^2 X^2 X^3+X^2 X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^2 0 X^3 0 0 0 X^3 X^2 X^3+X^2 X^2 X^2 X^3+X^2 X^2 X^3+X^2 X^2 X^3+X^2 X^3+X^2 X^2 X^3+X^2 0 0 X^3 0 0 X^3 X^3+X^2 X^3 X^3+X^2 X^3 0 X^2 X^2 X^3 X^3+X^2 0 X^2 X^3+X^2 X^2 0 X^3 0 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^2 0 X^3+X^2 0 X^3 X^3 0 X^3 0 X^3+X^2 0 X^3 X^3 X^2 X^3+X^2 X^3 X^3+X^2 0 X^2 0 0 0 X^3 0 X^3 X^3 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 X^3 X^3 0 0 0 0 0 0 X^3 0 X^3 X^3 X^3 X^3 0 X^3 X^3 X^3 0 0 0 X^3 X^3 X^3 X^3 X^3 X^3 0 X^3 0 X^3 X^3 X^3 0 0 0 0 0 X^3 0 0 X^3 0 X^3 X^3 0 0 0 0 X^3 0 X^3 X^3 0 0 X^3 X^3 0 0 0 0 0 0 0 0 0 X^3 X^3 X^3 X^3 X^3 0 X^3 0 0 X^3 0 X^3 0 X^3 0 0 X^3 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 X^3 0 X^3 0 X^3 0 X^3 X^3 0 0 X^3 0 0 0 0 0 0 0 0 0 0 X^3 X^3 0 X^3 X^3 0 X^3 X^3 0 0 0 X^3 X^3 0 X^3 0 X^3 0 X^3 0 X^3 0 X^3 0 0 X^3 X^3 0 X^3 0 X^3 0 0 0 0 X^3 generates a code of length 88 over Z2[X]/(X^4) who´s minimum homogenous weight is 83. Homogenous weight enumerator: w(x)=1x^0+214x^83+235x^84+508x^85+494x^86+550x^87+363x^88+420x^89+494x^90+326x^91+163x^92+164x^93+27x^94+90x^95+3x^96+28x^97+6x^98+4x^99+2x^100+2x^102+1x^126+1x^128 The gray image is a linear code over GF(2) with n=704, k=12 and d=332. This code was found by Heurico 1.16 in 1.09 seconds.