The generator matrix 1 0 1 1 1 X^2+X 1 1 X 1 1 X^2 X^2+X 1 X^2+X 1 1 1 0 1 1 1 1 X^2 X^2 X^2+X X^2 X 0 X^2+X X^2 X 1 1 1 1 1 1 1 1 1 1 X^2 X 1 X^2 X X^2 1 1 X 1 1 1 X X^2 1 1 X 1 1 X^2+X X X 1 X^2 0 1 1 1 1 1 1 1 1 1 0 0 1 0 1 0 1 1 0 1 1 X^2+X X^2+X+1 1 X^2 X+1 1 X X^2+1 1 1 0 1 X+1 0 X+1 1 X 1 X 1 1 1 1 1 1 1 1 1 1 0 X^2+X X^2 X X+1 X^2+1 0 X^2+X 0 X^2+X 1 1 X^2+1 1 1 1 X^2 1 1 X^2 X^2+X+1 0 1 1 X^2+X+1 0 1 X X^2+1 1 1 1 1 1 1 X X+1 X 0 0 X+1 X+1 X^2+X X^2 X^2 1 1 1 1 0 1 X^2 0 0 X 0 X^2+X 0 X X^2 X X^2+X 0 X^2+X X^2 X^2 X X^2 X X X^2 X^2+X X^2+X X^2 0 X^2+X 0 0 X X 0 0 X X 0 0 X X X^2 X^2 0 0 X X 0 0 X^2 X^2+X X^2+X 0 X^2+X X^2+X X^2 X X^2+X X^2+X X^2 X^2 0 X^2 X X X^2+X X^2+X X^2 X X X 0 X^2 X^2 0 0 X X^2+X X^2+X 0 X^2 X X 0 X X^2 X 0 X 0 0 0 X^2 0 0 0 X^2 X^2 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 0 X^2 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 0 X^2 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 X^2 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 0 X^2 0 0 X^2 X^2 0 0 0 0 0 0 X^2 0 0 0 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 0 0 X^2 X^2 0 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 0 0 X^2 0 0 0 0 X^2 X^2 0 0 0 0 X^2 X^2 0 0 X^2 X^2 X^2 0 0 0 0 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 X^2 X^2 0 X^2 X^2 0 0 X^2 0 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 0 X^2 0 X^2 generates a code of length 84 over Z2[X]/(X^3) who´s minimum homogenous weight is 78. Homogenous weight enumerator: w(x)=1x^0+199x^78+423x^80+343x^82+251x^84+261x^86+339x^88+149x^90+31x^92+26x^94+8x^96+12x^98+1x^100+2x^102+1x^108+1x^120 The gray image is a linear code over GF(2) with n=336, k=11 and d=156. This code was found by Heurico 1.16 in 0.698 seconds.