The generator matrix 1 0 1 1 1 X^2+X 1 1 X^3+X^2 1 X^3+X 1 1 1 0 1 1 X^2+X X^3+X^2 1 1 1 1 X^3+X 1 1 0 1 1 X^3+X 1 1 X^3+X^2 X^2+X 1 1 1 X^2+X 1 0 1 1 1 1 X^3+X^2 1 1 X^3+X 1 1 X X 1 X 1 X^2 X^3+X^2 X^3+X^2+X X X 1 X 1 1 1 1 1 X^3+X 1 1 1 1 0 X X^3+X^2 X^3 X 1 0 1 X+1 X^2+X X^2+1 1 X^3+X^2 X^3+X^2+X+1 1 X^3+X 1 X^3+1 0 X+1 1 X^2+X X^2+1 1 1 X^3+X^2 X^3+X^2+X+1 X^3+X X^3+1 1 X^2+X X+1 1 X^3+X^2 X^3+1 1 0 X^3+X^2+X+1 1 1 X^3+X X^2+1 0 1 X^2+1 1 X^3+X^2 X+1 X^2+X X^3+X^2+X+1 1 X^3+X X^3+1 1 X^2 1 1 X^3 X^2+X X^2 X X X 1 X^3+X^2 X^2+X X^3+X+1 X X+1 X^2+1 X^3+1 X^2+X 0 1 X^3+X^2+X X^3+X^2+1 X^2+1 X^2+1 X 1 1 1 X^3+X^2+X 0 0 0 X^3 0 0 0 0 0 X^3 X^3 0 0 X^3 X^3 X^3 0 0 X^3 X^3 0 X^3 X^3 0 0 X^3 X^3 0 X^3 0 X^3 X^3 0 0 X^3 0 X^3 0 0 X^3 X^3 X^3 0 0 0 0 X^3 X^3 0 0 X^3 X^3 0 0 X^3 X^3 0 0 X^3 X^3 X^3 X^3 0 X^3 0 X^3 0 X^3 0 0 0 X^3 X^3 0 0 0 X^3 0 0 0 0 0 X^3 0 0 0 0 X^3 X^3 X^3 X^3 0 X^3 0 0 X^3 X^3 0 X^3 X^3 0 0 0 X^3 0 X^3 X^3 0 0 X^3 X^3 X^3 0 0 X^3 X^3 0 0 X^3 0 0 X^3 X^3 0 0 X^3 X^3 0 0 X^3 0 X^3 0 X^3 X^3 X^3 0 X^3 0 0 0 X^3 X^3 0 X^3 0 X^3 0 0 X^3 X^3 0 0 0 X^3 0 0 0 0 0 0 X^3 0 0 X^3 0 0 0 X^3 X^3 X^3 X^3 X^3 0 X^3 0 X^3 0 0 0 X^3 X^3 X^3 X^3 0 X^3 0 X^3 X^3 0 X^3 0 0 0 0 X^3 X^3 0 0 X^3 0 X^3 X^3 X^3 X^3 X^3 0 0 0 X^3 X^3 0 0 X^3 0 X^3 0 X^3 0 X^3 X^3 X^3 0 0 0 X^3 0 0 X^3 X^3 0 X^3 X^3 0 0 0 0 0 0 0 X^3 X^3 X^3 X^3 0 X^3 0 0 0 X^3 0 X^3 0 0 X^3 X^3 X^3 0 X^3 X^3 X^3 0 0 X^3 0 X^3 0 X^3 X^3 X^3 X^3 0 0 X^3 0 X^3 0 X^3 X^3 X^3 0 0 0 0 0 X^3 X^3 0 0 X^3 0 X^3 X^3 X^3 X^3 0 X^3 X^3 0 0 X^3 X^3 0 X^3 X^3 0 0 0 0 0 X^3 0 0 generates a code of length 78 over Z2[X]/(X^4) who´s minimum homogenous weight is 72. Homogenous weight enumerator: w(x)=1x^0+25x^72+242x^73+212x^74+530x^75+333x^76+538x^77+416x^78+582x^79+347x^80+410x^81+127x^82+158x^83+58x^84+86x^85+11x^86+10x^87+2x^88+4x^89+1x^90+1x^92+1x^94+1x^120 The gray image is a linear code over GF(2) with n=624, k=12 and d=288. This code was found by Heurico 1.16 in 0.562 seconds.