The generator matrix 1 0 0 0 1 1 1 X 1 X^2+X 1 X^3+X X^3+X^2 1 1 X^3+X^2+X X 1 1 1 X^3 1 X^3+X X^3+X^2+X X 1 1 1 1 1 1 X^3+X X^3+X^2 X^2 1 1 X 1 0 1 X^3 X^3 1 X^3+X^2+X X^3+X 1 X^3+X 1 X^3+X^2+X X 1 X^3+X^2 1 X^2 1 X^3+X^2+X 1 0 X 1 X^3+X^2+X X^3+X^2+X 0 1 0 1 1 1 1 X^2 1 X^3+X^2+X 1 X^2 1 1 1 1 0 1 0 0 X^3 X^3+X^2+1 X^3+X+1 1 X^2 X^2 X^2 1 1 1 X^3+X+1 X^3+X 1 X^2+X+1 X^3+1 X^3+X^2+X+1 1 X^3+X^2 X^2 1 X^2+X X^3+X X^3+X^2+X X^3 X^3+1 X^2 X^3+X^2 X 1 1 X^2+1 X^3+X^2+1 1 X+1 1 1 X^3+X X 0 1 1 X^3+X^2 0 X^3+X+1 1 1 X^2+X 1 X^3+X^2+X+1 X X^3+X^2+X 0 X+1 1 1 X+1 X^2+X X 1 X^2 X^3+X X^3+X X^3+X^2 0 X 1 0 1 X^3+X^2 1 X^3+X^2+X+1 X^2+1 X^3+X+1 X^3+X^2 0 0 1 0 X^3+X^2 X^3 X^2 X^2 1 1 X^3+X+1 X^3+X+1 X^3+X+1 X+1 X^3+1 1 X^2+X X^2+X+1 X^3+X^2+1 X^2+X 1 X 1 X^2 X^3+X^2 X^3+X+1 1 X^3+X^2+X X^2+X X X^3 1 X^3+1 X^2+X+1 X^3+X X^2+1 X^3+1 X^3+X^2+X+1 X^2 X^3 1 0 X^2+X+1 X^3+X^2+X+1 X+1 1 X^3+X^2+X X^3+X^2+1 X^3+X^2+X X^2+1 X^2+X+1 X^2+X 0 1 X^3+X 1 X^3+X X^2+1 1 X+1 1 X X^3+X X+1 1 X^3+X^2 X^2+X X^3+X^2+X X X^3+X X^2+1 X+1 X^3+1 X^3+X^2 X^2+X+1 X^2+X+1 X^3+X X^3+X^2 0 0 0 1 X^2+X+1 X^3+X^2+X+1 X^3 X+1 X^3+X+1 X^3+X^2+X+1 0 X^3+X^2+1 X^2+X X^3+1 X^3+X^2+X X^3+X X^2+X X+1 0 X^3+X^2+1 1 X^3+X^2 1 1 1 X^3+X^2 X^3+1 X^3+X+1 X^3+X^2 X X^3+1 X^3+X^2+X+1 X^3 X+1 X^3+X+1 X^3+X^2+X X^3+X 1 X^3+X X^2+1 X^2+X+1 1 X^3+X X^3+X+1 X^2 X^3+X^2+1 1 X^2+X+1 0 X^3+1 X^3+X X^3+X^2+1 X^2+X X^3+X X^3+X^2 X^2+X 0 X+1 X^2 X^3+1 0 1 X^2+X X^3+X^2+X X^3 X^2+1 X^3+1 X X^3+X+1 1 X^3+X X^2+X X^2+X+1 X^2+X X^2+X+1 X^3+X^2+1 X X^3+X generates a code of length 78 over Z2[X]/(X^4) who´s minimum homogenous weight is 71. Homogenous weight enumerator: w(x)=1x^0+300x^71+1670x^72+2788x^73+4580x^74+5374x^75+7094x^76+7568x^77+8071x^78+6984x^79+6767x^80+5036x^81+4286x^82+2472x^83+1506x^84+600x^85+232x^86+92x^87+74x^88+6x^89+14x^90+10x^91+8x^92+1x^94+2x^105 The gray image is a linear code over GF(2) with n=624, k=16 and d=284. This code was found by Heurico 1.16 in 42.6 seconds.