The generator matrix 1 0 0 0 1 1 1 0 1 1 1 1 X X X 1 X X 1 0 1 1 X 1 1 1 1 0 1 1 X 1 1 X 0 0 0 0 1 0 0 1 X 0 0 X 1 1 0 0 0 1 0 1 1 X 0 0 X X 1 X 1 1 X X 1 0 1 0 0 0 1 1 1 X 0 X+1 X+1 1 1 X 1 1 1 1 1 0 X+1 X 0 1 X 0 X 1 X+1 1 1 X 1 1 1 1 1 X+1 1 1 0 1 X 1 1 X+1 1 X 1 X 0 X X 0 1 0 X 1 0 X+1 1 0 1 1 0 1 0 0 1 0 1 1 0 1 0 X+1 X+1 X X X+1 1 X X X+1 1 X+1 X+1 X 0 X+1 0 1 X 1 1 1 X X+1 1 X+1 X+1 0 0 1 X+1 X X+1 0 1 1 X X+1 X+1 X 1 1 X 1 1 X X+1 X+1 0 1 1 1 X X+1 1 1 0 1 X+1 0 0 0 1 1 0 1 1 1 0 1 X X+1 0 X+1 1 1 X+1 0 0 X 1 1 X+1 0 X X+1 X+1 1 0 X+1 X+1 1 X X 0 X X 0 X X+1 X X+1 X+1 X 0 1 1 0 X+1 1 X+1 X+1 1 0 X 1 X X X+1 X 0 0 1 1 1 X 0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X X X X X X X X X X X X X X X X X X 0 X X X 0 X X 0 X 0 X 0 0 0 X 0 0 0 0 X 0 X 0 0 0 0 0 0 X 0 0 0 0 0 0 X 0 0 0 X 0 X X 0 X X X X X X X X 0 0 X 0 X X X 0 0 0 X 0 X 0 0 X 0 X 0 0 X X X X X 0 0 0 0 X 0 0 X 0 0 X 0 X 0 0 0 0 0 0 X 0 0 0 0 0 0 X X X 0 X X 0 X X X X X 0 0 X 0 X 0 X X 0 X 0 X 0 X 0 0 X X X X 0 X 0 0 0 0 0 X X 0 0 X 0 X 0 X X 0 X X 0 0 0 0 0 0 0 0 0 X X X 0 X X X X X 0 0 X 0 X 0 0 0 0 0 0 0 X 0 0 X 0 X X 0 X 0 X X X 0 0 X 0 X 0 X X 0 0 0 X X X 0 X 0 0 X 0 X 0 0 X X X generates a code of length 67 over Z2[X]/(X^2) who´s minimum homogenous weight is 57. Homogenous weight enumerator: w(x)=1x^0+74x^57+122x^58+156x^59+222x^60+216x^61+257x^62+256x^63+238x^64+252x^65+232x^66+234x^67+223x^68+204x^69+218x^70+230x^71+197x^72+172x^73+133x^74+110x^75+126x^76+98x^77+43x^78+34x^79+11x^80+6x^81+16x^82+4x^83+5x^84+2x^85+2x^86+1x^88+1x^90 The gray image is a linear code over GF(2) with n=134, k=12 and d=57. This code was found by Heurico 1.16 in 67 seconds.