The generator matrix 1 0 0 0 0 0 1 1 1 0 1 1 X 1 0 1 1 1 1 0 X 0 X 1 1 1 X X X X 1 X 0 X 1 1 1 X X X 1 0 X 1 X 1 0 1 0 1 X X 1 0 1 X 1 1 0 1 0 1 1 X X X 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 X 1 1 1 1 1 1 X 1 X X+1 1 1 1 X 0 0 1 X 1 1 X X 0 1 1 X+1 0 X X+1 1 0 1 1 X 0 X X 1 X 1 X X X 1 0 1 X+1 X 1 1 1 0 0 0 1 0 0 0 0 0 0 0 1 1 1 X+1 1 X X+1 X+1 0 1 1 1 X X+1 X X 0 X+1 1 1 X 0 0 X X X+1 0 1 X+1 X X X 1 1 X+1 0 1 1 1 1 1 X 1 X X+1 1 X X+1 X 0 0 0 1 1 X+1 1 0 0 0 0 1 0 0 0 1 1 1 X 1 X+1 X+1 X+1 0 X 0 X+1 X+1 1 X X+1 0 X X+1 1 0 X X X+1 X+1 0 X 0 0 X+1 X 0 0 0 1 X+1 X+1 1 X+1 X+1 0 1 0 1 1 1 1 X 0 X+1 X 1 0 X+1 X+1 0 1 X+1 X 0 0 0 0 0 1 0 1 1 0 X+1 X 0 X X+1 1 X X+1 0 X 1 X 1 0 X+1 X+1 1 X+1 X+1 X X+1 1 X 1 X+1 0 X 0 0 X+1 0 X+1 X+1 1 X 1 X 0 X 1 0 X X 0 X+1 0 X 1 X+1 0 X+1 X+1 0 0 1 X+1 X+1 0 0 0 0 0 0 1 1 0 X+1 X+1 1 X X+1 X+1 X X+1 1 0 0 X+1 X 1 X+1 0 0 1 0 X 0 1 0 0 1 0 X 0 X X+1 X+1 1 1 0 1 X 0 0 1 X+1 X X 0 0 X 1 X+1 0 1 X+1 X+1 X 1 1 0 0 X X+1 0 0 0 0 0 0 0 X 0 X X X 0 X X 0 X X 0 0 X 0 X X 0 0 X 0 0 0 X 0 X 0 X X X X 0 0 0 0 X 0 X X X 0 0 0 X X X 0 X X X X 0 0 X 0 X 0 0 X X 0 0 0 0 0 0 0 0 X 0 X 0 X X 0 0 0 0 X X X 0 X X 0 0 X X X X 0 0 0 X 0 0 X 0 X 0 0 X 0 X 0 X X X X X 0 0 X 0 0 0 0 0 X X X 0 0 0 X 0 0 X generates a code of length 67 over Z2[X]/(X^2) who´s minimum homogenous weight is 54. Homogenous weight enumerator: w(x)=1x^0+75x^54+136x^55+263x^56+352x^57+423x^58+550x^59+656x^60+692x^61+706x^62+858x^63+870x^64+940x^65+1063x^66+1062x^67+1084x^68+1022x^69+965x^70+892x^71+755x^72+768x^73+627x^74+466x^75+370x^76+280x^77+206x^78+114x^79+86x^80+36x^81+31x^82+18x^83+10x^84+6x^85+1x^112 The gray image is a linear code over GF(2) with n=134, k=14 and d=54. This code was found by Heurico 1.16 in 75.8 seconds.