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 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 X 1 1 X^3+X^2 X 1 1 X^2 1 0 X 1 1 X^2 1 1 1 X X X 0 X 0 X 0 X^3 X^3+X X X^2 X^2+X X^2 X^3+X^2+X X^2 X^3+X^2 X^3+X^2+X X^3+X^2+X 0 X^3+X^2 X X^3+X^2+X X 0 X^3 X^3+X X^2+X X^2 X^2 X^2+X X^3+X 0 X^3+X^2+X X^3+X^2 X X^2 X^3+X^2+X X^3 X^2 0 X^3+X^2+X X^2 X X^3 X X^3+X^2+X X^3+X^2 X^2 X X^3+X X^2 X^3+X^2 X^2+X X^3+X^2+X X^3+X 0 X^3 X X^2+X X^3+X^2+X X^3+X^2 X^3 0 X X^2+X X^3+X^2 X^3+X^2 X X^2+X X X^3+X^2+X X^3+X X^2+X X^2 X^3+X^2+X X^2+X X^3+X X^2+X X^3+X X^2+X 0 0 X X X^3+X^2 X^3+X^2+X X^2+X X^2 X^2 X^3+X^2+X X 0 X^3 X^3+X^2+X X^3+X X^2 0 X^3+X X X^2 X^3+X^2+X X X^3+X^2 X^3+X^2 X^3+X^2+X 0 X^2+X X^3 X^3 X^2+X X^3+X X^3+X^2 X^2+X X X^3+X^2 X^3+X^2 0 0 X^2 X^2+X X^3+X^2+X X X^3+X^2 X X^2+X 0 X^3+X X^3+X^2 X^3+X^2 X X X^3+X^2+X X^3+X^2+X X^3+X^2+X X^3+X^2+X X^3 0 X^3+X^2 X^3+X X^3+X X^3 0 X^2+X X^3 X^2 X^3+X^2 X^2+X X^2+X X^3+X X X X X^3 X^3 X^3+X^2+X 0 0 0 0 0 0 X^3 0 0 X^3 0 X^3 0 X^3 X^3 X^3 X^3 0 X^3 0 X^3 0 X^3 0 0 X^3 0 X^3 0 0 0 X^3 X^3 X^3 X^3 X^3 0 0 0 0 X^3 0 0 0 X^3 X^3 0 X^3 X^3 X^3 X^3 0 0 X^3 0 X^3 0 X^3 0 X^3 0 0 X^3 X^3 0 X^3 0 X^3 0 X^3 0 X^3 0 0 0 0 X^3 X^3 0 0 X^3 0 0 0 0 X^3 X^3 X^3 X^3 X^3 X^3 0 0 0 X^3 0 X^3 X^3 X^3 0 0 X^3 X^3 X^3 0 0 0 0 X^3 X^3 0 X^3 0 0 0 0 0 X^3 0 X^3 X^3 0 X^3 0 X^3 0 X^3 X^3 X^3 0 X^3 0 0 0 0 X^3 X^3 X^3 0 0 0 X^3 X^3 X^3 X^3 0 0 X^3 X^3 X^3 X^3 0 0 X^3 0 X^3 X^3 0 0 generates a code of length 78 over Z2[X]/(X^4) who´s minimum homogenous weight is 73. Homogenous weight enumerator: w(x)=1x^0+320x^73+129x^74+476x^75+337x^76+544x^77+619x^78+568x^79+318x^80+328x^81+111x^82+172x^83+14x^84+112x^85+5x^86+32x^87+1x^88+8x^89+1x^132 The gray image is a linear code over GF(2) with n=624, k=12 and d=292. This code was found by Heurico 1.16 in 143 seconds.