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 X^2 X X X X 1 X 1 0 0 0 0 1 1 0 1 X 1 1 X^2 X 1 1 1 1 1 X X^2 1 X 0 X X^2 1 1 1 1 1 0 X 0 0 0 0 0 0 0 X^2+X X X X X X^2 X^2+X 0 X X X^2+X X^2 X^2+X X X^2 X X 0 0 X^2+X X^2 0 X^2 X X^2+X X X X 0 X^2 X^2 X^2 X^2+X X^2 0 X^2 X X^2 X X^2+X 0 X^2+X X X^2 X^2+X X 0 X X^2+X X^2 0 X^2+X X X X^2 X 0 X^2+X X^2 X^2 X^2 X^2+X 0 0 0 0 X 0 0 0 X X^2+X X X^2 X X^2+X 0 0 X X X^2 X^2+X X X^2 X X X X X^2 X^2 0 X^2+X X 0 0 X^2+X X X^2+X X X X X X X X^2+X X 0 X X^2 X^2+X X 0 X^2 X 0 X^2+X 0 X^2 X^2 X X^2 0 X^2+X 0 X^2+X X 0 X^2+X 0 X^2 0 X X^2+X 0 X^2 X 0 0 0 0 X 0 X X X 0 X^2+X X^2 X X^2+X 0 X 0 X X X^2+X 0 0 X^2 X X X^2+X X^2 0 X^2+X X^2 X^2+X X^2 X 0 0 X 0 X^2 X^2 X^2+X 0 X^2 X^2+X 0 X^2 0 X^2+X X^2 X X X 0 X X^2 X^2 X X^2+X X X^2 X^2+X X X^2 X X^2+X 0 X^2+X X 0 X X^2 X^2+X 0 0 0 0 0 0 0 X X 0 X X^2+X X 0 X X^2 X^2+X X^2+X X 0 X 0 0 X^2 X^2 0 X^2+X X X^2+X X^2 0 X^2+X 0 X^2+X X^2 0 X^2+X X^2+X X^2 0 X^2+X X^2+X X^2 X 0 X^2 X^2 X X^2 X^2 0 0 X^2 X X X^2 0 X^2 X^2+X X X^2 X^2 X^2+X 0 X^2 X^2+X X X^2+X 0 0 X 0 X X^2 X^2+X 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 0 0 0 0 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 0 0 X^2 0 X^2 0 0 0 X^2 X^2 0 X^2 0 0 X^2 X^2 0 X^2 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 0 X^2 0 generates a code of length 73 over Z2[X]/(X^3) who´s minimum homogenous weight is 62. Homogenous weight enumerator: w(x)=1x^0+38x^62+70x^63+144x^64+222x^65+231x^66+450x^67+204x^68+670x^69+217x^70+992x^71+241x^72+1348x^73+215x^74+1094x^75+197x^76+682x^77+165x^78+292x^79+174x^80+158x^81+96x^82+88x^83+49x^84+46x^85+56x^86+22x^87+12x^88+8x^89+5x^90+2x^92+2x^93+1x^106 The gray image is a linear code over GF(2) with n=292, k=13 and d=124. This code was found by Heurico 1.16 in 6.52 seconds.