The generator matrix 1 0 0 0 1 1 1 X^2 1 1 X^2 1 0 1 X^2+X X^2 1 1 1 0 1 1 1 X^2 X 1 1 X^2 X^2+X 1 1 1 X^2 1 1 1 1 X^2 1 X X^2 X^2 1 X^2+X 1 1 1 1 X^2 X^2+X 1 X^2 X^2+X X 1 1 1 1 0 X^2+X X^2+X X^2 X^2+X 1 1 X 1 X^2 1 1 1 0 1 X X^2+X 0 X^2 1 X^2+X 1 1 X^2+X 0 X^2+X X 0 1 0 0 0 0 X^2 X^2 X+1 X^2+X+1 1 X^2+1 1 X+1 1 X^2+X X 1 1 1 X^2+X+1 0 X+1 X^2+X 1 0 X^2 1 X^2+X X^2 X^2+X+1 X^2 X X+1 X^2+X X X 1 X+1 X^2 X 1 X^2+1 X^2 X X+1 X+1 0 1 X^2+X X+1 X^2+X 1 1 X^2+1 X^2+X X^2+X 0 1 X^2+X 0 1 X X^2+1 X^2+X+1 1 X^2 0 X+1 X^2+X+1 0 1 0 1 1 1 1 0 1 X^2+X X^2+X 1 X^2+X 0 X 0 0 1 0 0 X^2+1 1 1 0 X^2+1 X+1 X^2 X 1 X^2+X+1 X^2+X X X^2+X X^2+X+1 X^2+1 1 X+1 X^2 1 X^2 X^2+X+1 X^2+X 1 1 X^2+1 X X+1 0 0 X^2 X^2+X X^2+1 X X 1 1 X^2 X^2+1 0 X+1 X+1 X 1 1 X X^2+X+1 1 X X 1 X^2+X+1 X^2+X X^2+X 1 1 1 0 1 X^2+X+1 0 X^2+X+1 X+1 1 0 1 0 X+1 X^2+X+1 X X^2 X+1 X^2+1 X^2+X 1 X^2+X+1 1 1 X^2 X^2+X 1 0 0 0 1 X+1 X^2+X+1 0 X+1 X^2 X^2 0 X+1 X^2+1 X+1 X^2+1 1 X 0 X^2+X+1 X X 1 X^2+1 X X X^2+X X+1 X^2+X+1 1 1 0 X^2 1 X^2+X X^2+X X^2+X+1 0 X+1 X^2+X+1 0 X^2+X+1 X^2+X X^2 1 X+1 X^2 X^2+X X X^2+1 1 X+1 X X+1 0 X^2+X+1 X^2 0 1 X^2+X+1 X^2+X+1 X^2+X+1 X+1 X+1 X^2+X X^2+X+1 X^2 X^2+X+1 X X^2 X^2 X X 0 X^2+1 X+1 X+1 X X+1 1 X^2+1 X^2+1 X^2+X 1 1 X^2+1 0 0 0 0 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 0 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 X^2 0 0 X^2 0 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 0 0 0 X^2 0 X^2 0 X^2 X^2 0 0 0 0 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 0 0 0 0 X^2 X^2 0 X^2 0 0 X^2 X^2 generates a code of length 85 over Z2[X]/(X^3) who�s minimum homogenous weight is 78. Homogenous weight enumerator: w(x)=1x^0+522x^78+1178x^80+1480x^82+1280x^84+1155x^86+933x^88+734x^90+483x^92+252x^94+116x^96+46x^98+5x^100+3x^102+4x^104 The gray image is a linear code over GF(2) with n=340, k=13 and d=156. This code was found by Heurico 1.16 in 61.5 seconds.