The generator matrix 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 1 1 X 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 1 X^3 1 1 1 1 X 1 X^3 1 X 1 X X 1 X^3 1 1 X^2 1 1 1 1 1 X 0 X 0 X^3+X^2+X X^2 X^2+X X^3+X^2 X 0 X^2+X X^3 X^2+X X^3+X X^2 X^2 X 0 X^2+X X^2 X^3+X X^3 X^3+X X^3 X^3+X X^2+X 0 X^3+X X^2 X X^3 X 0 X^2+X X X^3+X^2 X^2 X^3+X^2+X X^2+X X^3+X X^3+X^2+X X^3 X^3 X^3+X X^2+X 0 X^3+X X^3+X^2 X^3+X X^2+X X^3+X^2 X^3 X^3+X X^3+X X^3+X^2 X^3+X^2 X X^3+X^2+X X^3 X^3+X^2+X X^2+X X^3+X^2 X^3 X X^2+X X^3+X X^3 0 X^3 X^2 X^2 X^3+X^2 X^3+X^2 0 X^2+X X X^3+X X^2+X X^3+X X^3+X^2+X 0 0 X^3+X^2 0 X^2 0 X^3 0 X^2 X^2 X^3 X^3+X^2 X^3+X^2 X^3+X^2 0 X^2 0 X^3+X^2 X^3 X^3+X^2 X^2 X^3 X^2 0 0 0 X^3+X^2 X^3+X^2 0 X^2 X^2 0 X^3 X^3+X^2 0 X^2 X^3+X^2 X^2 X^3 X^2 X^2 0 X^2 0 X^3 X^3 X^2 0 X^3+X^2 X^3 X^3+X^2 X^3+X^2 X^3 0 X^3+X^2 0 X^3+X^2 X^3 X^3+X^2 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^3 X^3 0 0 X^3 0 X^3+X^2 X^3 X^2 X^3+X^2 0 X^2 0 X^3 X^3+X^2 X^3 0 0 0 X^3+X^2 0 X^3 X^3 X^2 X^2 X^2 X^2 0 0 X^2 X^3+X^2 X^2 X^3 X^3+X^2 X^3+X^2 X^3 0 X^3+X^2 X^3+X^2 X^3 0 X^3+X^2 X^2 X^3+X^2 X^3+X^2 0 X^3 0 0 X^3 X^3 0 X^3+X^2 X^2 X^3 X^3 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 0 X^3 X^3+X^2 0 X^2 X^3 X^3+X^2 X^3 0 X^2 X^3+X^2 X^2 X^3+X^2 0 X^3 0 X^3+X^2 X^3+X^2 X^2 X^3+X^2 X^3 X^3+X^2 X^3+X^2 X^3 X^3 X^3+X^2 X^3 X^2 0 X^3+X^2 0 0 0 0 X^3 X^3 X^3 X^3 0 0 0 X^3 0 X^3 X^3 X^3 0 0 X^3 0 0 X^3 0 0 X^3 0 X^3 X^3 0 X^3 X^3 X^3 X^3 X^3 0 0 X^3 0 0 0 X^3 X^3 0 X^3 X^3 X^3 0 0 0 0 X^3 0 0 0 X^3 X^3 X^3 0 X^3 0 0 X^3 0 0 X^3 X^3 X^3 X^3 0 0 0 X^3 X^3 0 0 X^3 0 X^3 X^3 generates a code of length 79 over Z2[X]/(X^4) who´s minimum homogenous weight is 73. Homogenous weight enumerator: w(x)=1x^0+128x^73+114x^74+274x^75+265x^76+434x^77+553x^78+712x^79+527x^80+428x^81+228x^82+162x^83+54x^84+104x^85+20x^86+30x^87+10x^88+20x^89+12x^90+4x^91+6x^92+6x^93+2x^95+1x^100+1x^134 The gray image is a linear code over GF(2) with n=632, k=12 and d=292. This code was found by Heurico 1.16 in 1.16 seconds.