The generator matrix 1 0 0 1 1 1 X X^3+X 1 1 1 X^3+X^2 1 X^3+X^2+X 1 1 X^3 1 X^2 1 0 1 X^3+X X^3+X^2+X 1 X^3+X^2 1 1 X^3+X^2 1 1 X^3+X^2+X 1 1 0 1 X^2 X^3 X^3+X 1 1 X^3+X^2 1 1 X X^2+X 1 X 0 1 X^2+X 1 1 1 X^3 X^3+X^2+X 1 1 X 1 0 X^3 1 X^3+X^2+X 1 0 1 1 X^2+X X^3+X^2 X^2+X 1 1 1 X^3+X^2 1 X^3+X^2 1 1 0 1 0 0 X^2+1 X+1 1 X^3 0 X^3 X^3+1 1 X^3+1 1 X^3+X^2 0 1 X^2+1 X^2+X X^3+X^2+X+1 1 X^2 1 1 X^3+X^2+1 X^2+X X^3+X^2+1 1 1 X^3+X^2+1 X 1 X^3+X X^3+X^2+X 0 X^3+X^2 1 1 1 X^3+X X^2 X^2+X 0 X^2 1 X^3+X X^2+X 1 1 X^3+1 X^2 1 X^2+X+1 X^3+X 1 1 X^3+X+1 X^3+X^2+X+1 1 X 1 1 X^3+X^2+X+1 X X+1 X X^3 X^3+X X^3+X X 1 X^3 X^3+1 X^3+1 0 X^3+X^2+X 1 X^3+X^2+1 0 0 0 1 1 1 0 X^2+1 1 X X^3+X^2+X+1 X^2+X X+1 X^3+X^2+X+1 X^3+X^2 X^3+1 X^2 X^3+X^2+X X^2+X 1 X^2+X+1 X^2+X+1 X^3+X^2+X+1 X^3+X X^2+1 X^2+1 1 X^3 0 X^3+X^2+X X^3+X+1 X^2 X^3+X^2+X+1 X^3+X^2+1 X^3+1 1 X^2 X^3+1 X^2+1 X^3+X^2+X X^3 X^3+1 1 X X+1 X^3+X^2+X+1 1 X^3 X^2 X^2 X^3+X^2+X 1 X^2+1 X^3+1 X^3+X+1 0 X^3+X^2+1 X^3+X+1 X^3+X+1 X^2+X+1 X^3+X^2+X+1 X^3+X^2+X X 0 1 X^3+X^2 1 X^3+X X^3+X 1 1 X^3+X^2+X X+1 X^2+X+1 X^3 1 X^3+X^2+X X^2+X X^3+X^2+X 0 0 0 0 X X^3+X X^3 X^3+X X^3+X X^3+X X X^3+X^2+X X^3 X^2 X^2+X X^3+X^2 X^2+X X^2 0 X^3+X^2 X^2+X X^3+X X^3 X^2+X X^3+X^2 X^3+X^2 X^3+X X^2+X X^3+X^2 X X^3+X X^3+X^2+X 0 X X^2 X^2+X X^2 X^2+X X^3 X^2 X^3 X^3+X^2+X 0 0 X^3+X^2 X^3+X X^3+X X X^3 X^3+X^2 X^3+X 0 X^2+X X^3+X X^3+X^2 X^3+X^2+X X^3 X^3 X^2 X^2 X^3+X X^3+X^2 0 X^2+X X^3+X^2+X 0 X X^2+X 0 X^2 X^2+X X^3 X^3+X^2+X 0 X^2+X X^3+X X^2 X^3 X X^3 generates a code of length 79 over Z2[X]/(X^4) who´s minimum homogenous weight is 72. Homogenous weight enumerator: w(x)=1x^0+127x^72+730x^73+1565x^74+2216x^75+2627x^76+3538x^77+3638x^78+4150x^79+3928x^80+3606x^81+2446x^82+1788x^83+1071x^84+598x^85+335x^86+190x^87+89x^88+56x^89+27x^90+24x^91+12x^92+5x^94+1x^96 The gray image is a linear code over GF(2) with n=632, k=15 and d=288. This code was found by Heurico 1.16 in 17 seconds.