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 1 1 1 1 1 1 1 1 1 1 1 1 1 X^2 1 1 1 1 1 1 0 1 X 1 1 1 1 0 X 0 X 0 0 X X^2+X X^2 X^2+X 0 X^2+X X^2 0 X X^2+X 0 X X^2+X 0 X X^2 X^2 X^2+X X^2+X 0 X^2+X X^2 X^2 0 X^2+X X^2+X 0 X^2 X^2+X X X^2 X^2+X X^2 X 0 X^2+X X 0 0 X X^2+X X^2 0 X X X^2+X 0 X X 0 X^2 X^2 X^2+X 0 X^2+X X^2 X X^2 X^2 X^2 X 0 0 0 X^2+X X^2+X X^2 X^2+X X^2 X 0 0 X^2+X 0 0 X X 0 X^2+X X X^2 X 0 0 X X 0 X^2+X X^2 X X^2+X X^2 0 0 0 X X^2+X 0 X^2 X^2+X X^2+X X^2 X X X^2 0 X 0 X X 0 X^2 X^2+X X^2+X X 0 X^2 X^2+X X^2 X^2+X X^2 0 X^2 X^2+X 0 X^2 X 0 X X X^2 X^2+X X^2+X 0 X^2 X X X^2+X 0 X^2+X X^2+X X^2+X X^2 X^2+X X X X X X^2 X X 0 0 0 0 X^2 0 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 X^2 X^2 0 X^2 0 0 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 0 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 X^2 X^2 0 0 0 0 0 X^2 0 X^2 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 0 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 0 0 X^2 0 X^2 0 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 0 0 X^2 X^2 0 0 0 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 0 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 generates a code of length 79 over Z2[X]/(X^3) who´s minimum homogenous weight is 73. Homogenous weight enumerator: w(x)=1x^0+40x^73+34x^74+40x^75+61x^76+170x^77+54x^78+282x^79+40x^80+156x^81+20x^82+44x^83+19x^84+18x^85+14x^86+18x^87+6x^88+6x^90+1x^152 The gray image is a linear code over GF(2) with n=316, k=10 and d=146. This code was found by Heurico 1.16 in 0.442 seconds.