The generator matrix 1 0 0 1 1 1 X^2+X 1 X 1 1 1 0 X 0 X 1 1 1 0 1 X 0 0 1 1 1 1 X^2 1 X^2+X 1 X 1 1 X^2+X X^2+X 1 X^2 1 X 1 1 1 X^2 0 1 X^2+X 1 1 1 X^2 1 X^2 0 X 1 1 1 X^2 X^2 1 X X X^2+X X 1 X 1 1 1 X^2+X 1 1 1 X 0 1 X X^2 1 1 1 1 1 1 X 0 1 0 0 1 X+1 1 X^2+X 0 X+1 X^2+X 1 1 1 X^2+X 1 X^2+1 X^2+X+1 0 1 X^2+X 1 1 X^2 X^2+X+1 X^2+X X^2+1 0 1 X^2 1 X^2+X 0 X+1 X^2+1 1 1 X 0 X^2+1 1 X X^2+X+1 1 1 X^2+X 1 0 X^2+X+1 X^2+X+1 X 1 X+1 1 X^2+X X^2 X^2+X+1 X+1 X^2 1 X X^2+1 1 1 1 1 X^2 1 X^2 X^2+X 0 X X X+1 X^2+X+1 1 1 X^2 1 1 X^2+X+1 X^2 X^2 X^2+X+1 X^2+X+1 0 1 0 0 1 1 1 0 1 1 1 X^2+1 0 X^2 1 X^2 1 X^2+X X^2+X X+1 X^2+X 1 X^2+1 X^2+X+1 0 1 0 X^2+X 1 X^2+X+1 X^2 X+1 X^2+X+1 X^2 1 X^2+1 X^2 X^2+1 X^2 X+1 1 1 X^2+X X X^2 X^2+X+1 1 1 X 1 X^2+1 X^2+X X^2+X+1 X+1 X^2+X+1 X^2+1 1 1 1 X^2+X X^2 X^2 1 X^2 X X+1 0 0 X 0 X^2+X+1 X^2+X X^2 1 X^2+X+1 0 X X^2+X X^2 X+1 X^2 X X^2+1 X^2+1 X^2 X^2+1 X^2+X X 1 0 0 0 X 0 0 X^2 X^2 X^2 X^2+X X X X^2+X X X 0 X^2+X X^2 X 0 0 X^2+X X X^2+X 0 X^2 X^2+X X^2+X 0 X 0 X^2 X^2+X X^2 X^2+X X X 0 X X^2+X X^2 X X^2+X X X X^2 X^2+X 0 X^2 0 X^2 0 X X^2 X^2+X X^2+X X 0 0 X^2+X X^2 X^2 X X^2+X X^2+X X^2 X^2+X 0 X^2 X^2 X^2 X^2+X X^2 X^2 X^2+X X^2 X^2 X^2 X^2 X^2 X^2+X X^2 X 0 X^2 X 0 0 0 0 0 X X^2 X X^2+X X^2+X X^2 X X^2+X 0 X 0 X^2+X X^2 0 X^2 X^2 X^2 X X^2 X X X X^2+X X^2+X X^2+X 0 0 X^2 0 0 X^2 X X^2 X X^2 0 0 0 X X 0 X X^2+X 0 X X^2 0 X^2 X X^2+X X^2+X X^2+X X^2+X X X^2 X^2+X 0 X^2+X 0 0 X^2+X 0 X^2+X X 0 0 X X^2 X X^2 0 X^2 X^2+X X^2 X X^2 0 X^2 X^2+X X^2+X X X 0 generates a code of length 87 over Z2[X]/(X^3) who´s minimum homogenous weight is 79. Homogenous weight enumerator: w(x)=1x^0+152x^79+255x^80+462x^81+591x^82+610x^83+689x^84+614x^85+625x^86+692x^87+656x^88+490x^89+535x^90+440x^91+325x^92+340x^93+221x^94+140x^95+99x^96+94x^97+74x^98+38x^99+14x^100+14x^101+2x^102+8x^103+5x^104+2x^105+4x^108 The gray image is a linear code over GF(2) with n=348, k=13 and d=158. This code was found by Heurico 1.16 in 4.78 seconds.