The generator matrix 1 0 0 0 0 0 0 1 1 1 0 1 X 1 1 0 1 1 1 0 1 X 1 X 0 1 1 X 0 0 X 1 X 1 0 1 1 X 1 1 1 0 0 1 1 1 1 0 X 1 X 1 1 0 X 1 0 1 1 1 X 0 0 1 1 0 X 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 X X X 1 X+1 1 1 1 1 1 1 X+1 1 1 1 0 1 X 1 X+1 1 1 X 1 0 X 0 1 1 X+1 0 X X+1 0 X X+1 1 X X 1 0 X+1 1 X+1 1 X+1 X 1 1 X X+1 1 0 1 X 0 0 1 0 0 0 0 0 0 0 0 0 0 X 0 0 X 0 0 0 0 0 X X X X X 0 X X 0 X X X+1 X+1 1 X+1 X+1 1 X+1 X+1 1 X+1 X+1 1 1 1 1 1 1 X+1 X+1 X+1 1 X X 1 X+1 X 1 X X X+1 X X X+1 1 0 0 0 0 0 1 0 0 0 0 0 X X 1 1 X+1 X+1 1 1 X+1 X+1 1 X X+1 1 X+1 0 X X 0 X+1 0 0 1 X X 1 0 X 0 X 1 1 X+1 X X+1 X+1 X+1 X 1 X 1 X+1 1 0 0 X 0 1 1 X+1 0 0 X+1 X+1 X+1 1 1 1 X+1 0 0 0 0 0 1 0 0 X 1 X+1 1 0 1 1 1 X+1 X X+1 1 X 1 1 X 0 0 X 0 1 X+1 1 0 1 1 0 X 1 X+1 1 X X+1 X+1 X+1 X+1 X+1 0 0 1 X X+1 X 0 X 0 X 1 0 0 1 0 1 0 X 0 0 X 1 1 X X 0 0 0 0 0 1 0 X+1 1 0 1 X X+1 X+1 0 X X+1 X+1 X 0 X X+1 1 1 1 X X+1 X+1 X X+1 1 0 0 X X 0 1 0 X+1 0 1 1 0 X+1 1 X 1 0 X X+1 X+1 X 1 1 0 1 X X+1 0 X+1 1 0 X+1 X+1 X+1 X 1 1 X 0 0 0 0 0 0 1 1 X 1 1 X+1 X 1 X 1 X 0 1 1 0 1 1 0 X+1 1 X 0 X X+1 X+1 X 1 X X X+1 1 0 X X+1 0 0 X X+1 1 X 0 X+1 X+1 0 X+1 0 X+1 1 0 X X X X+1 X+1 1 X+1 1 X 1 1 0 X+1 X+1 generates a code of length 69 over Z2[X]/(X^2) who´s minimum homogenous weight is 56. Homogenous weight enumerator: w(x)=1x^0+73x^56+138x^57+260x^58+352x^59+489x^60+536x^61+608x^62+738x^63+769x^64+880x^65+936x^66+928x^67+977x^68+1000x^69+993x^70+1044x^71+898x^72+866x^73+744x^74+704x^75+655x^76+544x^77+438x^78+282x^79+210x^80+116x^81+116x^82+48x^83+23x^84+16x^85+1x^86+1x^120 The gray image is a linear code over GF(2) with n=138, k=14 and d=56. This code was found by Heurico 1.16 in 77 seconds.