The generator matrix 1 0 0 0 1 1 1 0 1 X X X^2+X 1 1 1 X^2+X 1 1 X^2+X 1 1 1 0 1 1 X^2+X X^2 X X X 1 X^2 1 X^2 1 X^2+X 1 0 1 X^2 X 1 0 0 1 1 X X^2+X X 1 1 1 X 1 1 1 X^2 1 X^2 1 0 0 1 1 1 1 1 0 X 1 0 1 0 0 0 1 1 1 X^2 X^2+X 1 1 X^2 X^2+X+1 1 X X+1 X X^2 X^2+X+1 1 X^2 1 X^2 X+1 1 1 1 X^2 1 X^2+X 1 X^2+X+1 1 1 X X^2 X 0 1 0 X^2 1 X^2+X X^2 X^2+1 1 1 X X^2+X+1 X^2 X^2+1 1 X X^2 1 X^2+X X^2+1 1 X^2 1 1 X+1 X^2 1 X+1 1 1 1 0 0 0 1 0 1 1 X^2 X^2+1 X^2+X+1 1 X^2 1 X^2+X X^2+1 X 1 X X^2 X^2+X X^2+X+1 X^2+X X^2+X+1 X+1 X^2+1 1 X^2 X^2 X+1 1 X+1 X^2 X X^2+X+1 X^2+X X^2+X+1 X^2+X X+1 0 1 X^2+1 1 X+1 X^2+X+1 1 X X+1 1 X^2+X+1 1 0 X^2 X^2+X X^2+X+1 0 X^2+X X+1 1 1 X X^2+1 X^2 1 X^2+X+1 X^2+X+1 1 X X^2+1 X^2+X X^2+X 0 0 0 0 1 1 0 X^2+1 1 X^2 1 X+1 X 1 X^2+X+1 X X^2+X+1 1 X 1 X+1 X X^2+X X X^2+X+1 X^2 X^2+X X+1 X^2+X X^2 X^2+X+1 1 X+1 X^2 X X+1 1 X 1 X^2 1 0 1 X^2 X^2+X+1 1 X^2+X+1 X X^2+X X^2+1 X X X^2+X+1 1 0 0 0 X^2 X^2+X 0 X 1 X^2 0 0 X+1 0 X^2+1 X+1 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2+X X X^2+X X X X X^2+X X^2+X X^2+X X X^2+X X^2+X X X^2+X X X^2+X X X X^2+X X^2 X X^2+X X^2 X^2 X^2 X^2+X X^2 X X X^2 X X X X X^2 X X^2 X X 0 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 0 0 0 0 0 0 X^2 0 0 X^2 X^2 0 0 0 X^2 0 X^2 0 0 generates a code of length 70 over Z2[X]/(X^3) who´s minimum homogenous weight is 60. Homogenous weight enumerator: w(x)=1x^0+106x^60+304x^61+667x^62+854x^63+1555x^64+1588x^65+2214x^66+2066x^67+3051x^68+2402x^69+3374x^70+2384x^71+2858x^72+2188x^73+2456x^74+1410x^75+1344x^76+704x^77+577x^78+300x^79+152x^80+96x^81+48x^82+20x^83+19x^84+14x^85+6x^86+6x^87+2x^88+2x^90 The gray image is a linear code over GF(2) with n=280, k=15 and d=120. This code was found by Heurico 1.16 in 44.9 seconds.