The generator matrix 1 0 0 0 0 1 1 1 0 X^2 1 1 1 0 0 X^2+X 1 X^2+X 1 1 X^2+X 1 X^2 1 0 X^2 0 1 1 X^2 X X^2+X 1 1 X^2+X 1 1 1 1 1 X 1 1 0 1 1 1 X 1 1 X 1 1 X^2 X^2 1 X^2 X^2+X 1 1 1 1 1 X^2+X X^2+X 0 1 X 0 1 0 0 0 0 0 0 X^2 0 0 X^2 0 0 X^2 X^2 X^2 0 X+1 X^2+X+1 1 1 1 1 1 1 1 X X^2+X+1 X 1 X^2+X X 1 1 1 X^2+1 X X+1 X 1 0 X^2+1 X^2 X X^2+X X^2+1 0 X^2+1 X^2+X+1 1 X^2 X 1 1 X^2+1 X 1 X^2+X X^2+X X^2+X 0 X 1 1 1 X^2+1 1 0 0 1 0 0 0 1 1 1 1 X^2 X+1 X^2+X+1 1 X^2+X X 0 X X 1 X^2+1 X^2+1 X^2+X X^2+1 X^2+X+1 0 1 X^2+X+1 X^2+X+1 1 X^2+X X X+1 X X^2+1 X^2+X 0 X^2+1 X^2 X^2+X 0 X^2+X 0 1 1 1 X^2+X+1 1 X^2+X+1 X X^2+X+1 X^2 X+1 X X X^2+X X 1 X^2+X X+1 X^2+1 X^2+X X^2+1 X^2 X^2+1 X^2+X X X^2+X 0 0 0 1 0 1 1 X^2 X^2+1 X^2+1 X 1 X X^2+X 1 0 X^2+X+1 1 X^2+1 X^2+1 X^2+1 X X+1 0 0 X+1 1 X^2+X 1 X X^2 1 X+1 X^2 X 1 X^2+X 1 X^2+1 X^2+1 1 X^2+X+1 X X+1 1 X^2+1 X^2+X+1 0 0 X^2+X+1 0 1 X^2+X X^2+X+1 X^2+X+1 X^2 1 X^2+X+1 X^2 0 X+1 X^2+X X^2 X^2 X X X^2+1 1 0 0 0 0 1 1 X^2 X^2+1 X^2+1 X X^2+X+1 X+1 X^2 X+1 X^2+X+1 1 0 X^2+X X^2+X+1 1 X 0 0 X+1 X^2+1 X^2+1 X+1 X^2 X X^2+X X+1 X+1 1 X X X+1 X+1 0 0 1 X^2+X 1 X^2 1 X^2+1 X^2+X X^2+1 X^2+X+1 X+1 X 1 X^2+1 X^2+1 X^2+X+1 1 X^2+X+1 0 X^2+X+1 X^2+1 X^2+X+1 X^2 X+1 0 X^2+X+1 X+1 1 X^2 1 0 0 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 0 X^2 0 X^2 0 0 X^2 0 0 0 X^2 0 0 0 X^2 0 0 X^2 0 X^2 X^2 X^2 0 0 0 X^2 0 X^2 X^2 generates a code of length 68 over Z2[X]/(X^3) who´s minimum homogenous weight is 58. Homogenous weight enumerator: w(x)=1x^0+246x^58+732x^59+1233x^60+1776x^61+2391x^62+3208x^63+4219x^64+4606x^65+5179x^66+5808x^67+5961x^68+6336x^69+5729x^70+4868x^71+4134x^72+3154x^73+2295x^74+1488x^75+944x^76+614x^77+336x^78+148x^79+73x^80+24x^81+12x^82+4x^83+10x^84+2x^85+4x^86+1x^88 The gray image is a linear code over GF(2) with n=272, k=16 and d=116. This code was found by Heurico 1.13 in 55.1 seconds.