The generator matrix 1 0 0 1 1 1 0 1 1 1 1 0 X 1 0 1 0 1 1 X 0 1 1 1 X 1 0 X 1 X 1 1 1 1 0 1 0 1 1 X 1 1 1 1 0 0 1 X 1 1 1 1 1 0 1 0 1 X 0 1 X 1 1 1 0 1 0 1 1 1 1 1 0 1 0 1 0 1 1 0 0 1 X+1 1 1 X 0 X 0 X+1 X+1 1 1 1 X 1 0 0 1 1 X 1 1 1 1 0 1 X+1 1 X+1 X 0 0 X+1 0 X 0 1 1 X 1 X X X 0 1 X 0 X+1 X 0 X+1 1 1 1 0 1 X 1 X X+1 1 X 0 0 0 1 1 1 0 1 0 1 X+1 X X 1 0 1 1 1 X+1 0 1 0 1 1 X+1 1 X+1 X 1 0 1 1 X+1 X+1 0 1 0 0 1 1 1 1 X X+1 1 1 0 X+1 1 X 0 X 1 1 X X+1 1 0 1 1 0 1 1 1 X 0 X X 1 X X 1 0 0 0 0 X 0 0 0 0 0 X 0 0 0 0 0 0 0 X 0 0 0 X 0 X 0 0 X 0 0 0 X X X 0 X X 0 X 0 X X X X X X X 0 0 0 X X 0 X X X X 0 X 0 X 0 X 0 0 0 0 X 0 X 0 0 0 0 0 0 0 X 0 0 0 0 0 0 X X X X 0 0 X 0 X X X X 0 0 X 0 0 0 X X 0 0 X 0 X X X 0 X X X X X X 0 0 X 0 0 X 0 X X 0 0 0 X X 0 X 0 X 0 0 X 0 0 X X 0 0 0 0 0 0 0 X 0 0 0 0 X 0 0 0 0 0 0 0 X 0 X X X X X X 0 0 X X 0 X 0 X X X X 0 X 0 X X 0 0 0 X 0 0 X 0 X X X 0 0 0 0 0 0 X X 0 X 0 0 X X 0 0 X 0 0 0 0 0 0 0 0 X 0 0 0 0 0 X 0 0 0 X X X 0 X X 0 0 0 X X X X X 0 0 X X X X 0 X 0 0 0 0 X X 0 0 X X 0 0 X 0 X 0 X X 0 0 0 X X X 0 X X X X 0 0 0 0 0 0 0 0 0 0 0 0 X 0 X X 0 0 0 X X X X X 0 0 X 0 0 X X 0 X 0 X 0 0 0 0 0 X X X X X X 0 X 0 X X X 0 X 0 0 0 X 0 0 0 X 0 0 0 X X X X X X 0 0 X X 0 0 0 0 0 0 0 0 0 0 X 0 0 X X X X X 0 X 0 X X X 0 0 0 0 X X 0 X 0 X X 0 X 0 0 0 X 0 X 0 0 X X 0 0 0 X 0 0 X 0 X 0 X X X 0 0 0 X 0 0 X 0 X 0 0 X X 0 generates a code of length 72 over Z2[X]/(X^2) who´s minimum homogenous weight is 60. Homogenous weight enumerator: w(x)=1x^0+27x^60+52x^61+89x^62+134x^63+166x^64+154x^65+205x^66+184x^67+224x^68+244x^69+254x^70+278x^71+220x^72+256x^73+206x^74+220x^75+209x^76+200x^77+169x^78+142x^79+115x^80+102x^81+69x^82+60x^83+42x^84+16x^85+16x^86+6x^87+10x^88+16x^90+10x^92 The gray image is a linear code over GF(2) with n=144, k=12 and d=60. This code was found by Heurico 1.16 in 2.9 seconds.