The generator matrix 1 0 0 1 1 1 X X^3+X 1 1 X^3 1 1 X^2 1 1 1 X^3+X X^2+X X^2+X 1 X^3+X^2+X X X^2+X 1 1 1 1 0 1 X 1 1 1 X^2+X 1 1 X^2+X X^2 X^3+X^2 1 1 1 X^2 X^2 X^2 1 X^3+X^2 X 1 X^3+X^2 1 1 0 1 1 X 1 1 1 1 X^2 1 1 1 1 1 1 X^2+X 0 X^2+X X^2 1 X^3+X^2 1 1 1 1 X 1 1 1 1 1 0 1 0 0 X^2+1 X+1 1 X^3 0 X^3+X^2+1 1 X^2 X+1 1 X^3+X X^3+X^2+X X^3+X^2+1 1 X^3+X^2+X 1 X^3+1 1 X^3+X 1 X+1 0 X^2+X+1 X^3+X^2 X^3+X^2+X X^3+1 1 X X+1 X 1 X^2+X+1 X^3+X+1 0 X^2 1 X^3+X^2+X X^2+X X^2+X+1 1 1 X^3+X X^3 X^3+X^2+X 1 X^2 1 X^2+1 X^2 1 X^2 1 0 X^3+X^2 X^3+X X+1 X^3+X X^3+X^2+X X^3 X^3+1 X^3+1 X^3+1 X^3+X^2+X X^3+X+1 X 1 1 X^3 0 1 X^3+1 X^3+X^2 X^2+X+1 X 1 X^3 X^2+X+1 0 X 0 0 0 1 1 1 0 X^2+1 1 X X^3+X X^2+X+1 1 X^3+1 X^2 X+1 X X^3+X+1 X^3+X^2 1 X^2+X+1 X X^3+X^2+X+1 1 0 X^3 X^3+X^2 X^3+X+1 X^3+X^2+X+1 1 X^2 X^2+1 X^2 X^3+X^2+1 X^3 X X^2+X X^3+X 1 1 X^2+X X X^2+1 X^2+X+1 X^3+X^2+1 X+1 1 X^3+X^2+X 1 X^3+X X^3+1 0 X^3+1 X^3+X^2+X+1 X^3+X^2+X X^3 X^3 1 X^3+X^2+X+1 X^3+X^2+1 X^2 X^3+X^2+X+1 1 X^2+1 X^2+X 1 X^2+X+1 X^3+X^2 0 1 X^3+1 0 1 X^3+X X^3+X^2+X X^3+X^2+X X^3+X^2+X X^3+X^2+X X^2 X^2+X 1 X^3+X^2+X+1 X^2 X^3+X^2 0 0 0 0 X X^3+X X^3 X^3+X X^3+X X^3+X X X^3 0 X^3+X^2 X^2+X X^3+X^2+X X^3 X^3+X^2 0 0 X 0 X^3 X^3+X X^3+X X^2+X X^2+X X X^3+X^2 X^2+X X X^3+X^2 X^2 X^3+X X X^3+X^2 X^3+X X^2 X^3 X^3+X^2 X^3+X X X^3+X^2 X^3 X^3+X^2+X X^3+X^2 0 X^3 X 0 X X^3+X X^2 X X^3+X^2 X^2 0 X^2+X 0 X^2+X X X^3 X^2 X^2+X X^2 X^3 X^2+X X^3+X^2+X X^2 X^2+X X^2 X^2+X X^2+X X^3+X^2 0 X X^2+X X^2 X^2+X X^2+X X^2 0 0 X X^3 generates a code of length 84 over Z2[X]/(X^4) who´s minimum homogenous weight is 77. Homogenous weight enumerator: w(x)=1x^0+142x^77+736x^78+1550x^79+2376x^80+2958x^81+3369x^82+3936x^83+3614x^84+3908x^85+2906x^86+2510x^87+1972x^88+1282x^89+741x^90+368x^91+190x^92+82x^93+58x^94+16x^95+27x^96+12x^97+4x^99+4x^100+6x^102 The gray image is a linear code over GF(2) with n=672, k=15 and d=308. This code was found by Heurico 1.16 in 14.2 seconds.