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^2+X 1 1 X^3+X^2 1 X^3+X 1 1 1 0 X^2+X 1 1 1 1 X^3 1 1 X^3+X^2+X 1 1 X^3+X^2 1 1 X^3+X 1 X^2 1 X 1 1 1 X^3+X^2 1 X^3 X^2 1 1 X^2+X 1 1 X^2 X^3+X^2 1 X 1 0 X^2 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 X+1 0 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 0 X+1 1 X^2+X X^2+1 1 X^3+X^2 X^3+X^2+X+1 1 X^3+1 1 X^3+X X^2+X X+1 1 1 0 X^2+1 X^3 X^3+X+1 1 X^3+X^2+X X^3+X^2+1 1 X^3+X^2 X^3+X^2+X+1 1 X^3+X X^3+1 1 X^2 1 X^3+X^2+X+1 1 X^3+X X^2+X+1 X^3+X^2 1 X^3+1 X 1 1 X^2 1 X^2+1 X X^2 X X 1 X+1 X X 0 0 X^3 0 0 0 0 0 0 0 0 0 0 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 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 0 0 0 0 X^3 X^3 X^3 0 X^3 X^3 0 0 0 0 X^3 X^3 X^3 X^3 0 0 X^3 X^3 0 0 0 0 X^3 X^3 X^3 0 0 0 X^3 0 X^3 0 X^3 X^3 0 0 0 0 X^3 0 0 0 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 X^3 X^3 0 X^3 X^3 0 0 0 X^3 0 0 0 X^3 0 0 X^3 X^3 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 0 0 0 0 X^3 0 0 0 0 X^3 X^3 0 X^3 X^3 X^3 X^3 0 0 X^3 X^3 X^3 0 X^3 0 X^3 0 X^3 0 0 X^3 0 X^3 0 X^3 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 X^3 X^3 0 X^3 0 X^3 0 X^3 0 0 X^3 0 X^3 0 X^3 0 X^3 X^3 X^3 X^3 0 0 0 X^3 X^3 0 X^3 0 0 X^3 X^3 0 X^3 X^3 X^3 0 0 0 0 X^3 0 X^3 X^3 X^3 0 X^3 0 X^3 0 X^3 0 X^3 X^3 X^3 0 X^3 X^3 0 X^3 0 0 0 0 0 X^3 X^3 X^3 X^3 X^3 0 0 X^3 X^3 X^3 0 X^3 0 0 0 0 X^3 X^3 X^3 X^3 0 X^3 0 X^3 0 0 X^3 0 0 X^3 0 X^3 0 0 X^3 0 X^3 X^3 X^3 X^3 X^3 0 0 X^3 0 0 0 X^3 0 0 X^3 X^3 X^3 X^3 0 0 X^3 X^3 X^3 0 X^3 X^3 X^3 0 0 X^3 X^3 0 0 X^3 X^3 0 generates a code of length 77 over Z2[X]/(X^4) who´s minimum homogenous weight is 72. Homogenous weight enumerator: w(x)=1x^0+264x^72+72x^73+807x^74+152x^75+745x^76+112x^77+791x^78+80x^79+687x^80+72x^81+189x^82+24x^83+91x^84+5x^86+3x^96+1x^104 The gray image is a linear code over GF(2) with n=616, k=12 and d=288. This code was found by Heurico 1.16 in 11.5 seconds.