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 X 1 1 1 1 X 1 X 1 0 0 1 1 1 0 1 1 1 1 0 0 X 1 X 0 1 0 X 1 X 1 0 1 0 X 0 X 0 0 X X^2+X 0 X^2 X^2+X X 0 X X 0 X^2 X X^2+X X^2 0 X^2 X X^2 X 0 X^2 X X^2+X 0 X^2+X X^2+X X^2 X^2 X X^2 0 X X^2+X X^2+X X^2+X X^2+X X^2 X^2 0 X^2+X X^2+X 0 X^2 0 0 X X X X 0 X^2+X X X^2 X X X 0 X X^2+X 0 X^2+X 0 0 X X 0 X^2+X X 0 X^2 X 0 X 0 X^2+X X^2 X^2+X X X X^2 X^2 X^2 X 0 X^2 X^2+X 0 X^2+X 0 0 X^2+X X X X^2 0 X X 0 X^2+X 0 X^2 X X 0 X X X 0 X X 0 X^2 X^2+X X^2+X 0 0 X^2+X X^2+X X X X^2 0 X X^2+X X^2 X X 0 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 0 0 X^2 X^2 0 X^2 0 0 0 X^2 X^2 0 0 X^2 X^2 X^2 0 0 X^2 0 0 0 X^2 0 X^2 0 0 X^2 X^2 0 0 X^2 0 0 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 0 X^2 0 0 0 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 0 0 X^2 0 X^2 X^2 0 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 0 X^2 0 X^2 0 0 X^2 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 0 0 X^2 X^2 0 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 0 0 0 0 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 0 0 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 0 X^2 0 0 0 X^2 X^2 0 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 0 0 0 X^2 0 X^2 0 X^2 0 0 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 generates a code of length 67 over Z2[X]/(X^3) who´s minimum homogenous weight is 58. Homogenous weight enumerator: w(x)=1x^0+99x^58+4x^59+235x^60+56x^61+288x^62+88x^63+402x^64+232x^65+572x^66+272x^67+538x^68+200x^69+360x^70+136x^71+243x^72+24x^73+157x^74+12x^75+97x^76+50x^78+17x^80+4x^82+2x^84+6x^86+1x^104 The gray image is a linear code over GF(2) with n=268, k=12 and d=116. This code was found by Heurico 1.16 in 2.14 seconds.