The generator matrix 1 0 1 1 1 X^2+X 1 1 X^2 1 1 X 1 1 X^2 X^2+X 1 1 1 X^2 1 1 X 1 1 1 0 1 X^2+X 0 1 1 1 1 1 0 1 1 1 X 1 1 1 1 X^2+X 1 X^2+X 1 1 X^2+X 1 1 1 1 0 1 0 1 X 1 X 1 0 1 1 X^2+X X^2 1 X 1 1 X X^2+X 1 1 0 1 1 X^2+X 1 1 1 X^2 1 1 0 1 1 0 X^2+X+1 1 X+1 X^2+X 1 1 X 1 X^2+1 X^2 1 1 1 X^2+X X^2+X+1 1 0 X^2 1 X^2+X+1 X 1 1 X 1 1 X^2+X+1 0 1 X X^2+1 1 0 X+1 1 1 X^2 X^2+X X^2+X+1 X^2+1 1 X^2+X 1 X^2+1 X 1 X X^2 X^2+X X^2+X 1 X 1 0 1 X^2 1 0 1 1 X+1 1 1 X 1 X^2+X 1 1 1 X^2 X^2 X X+1 X^2+X 1 X^2+X+1 X^2+X X^2 1 X^2+X+1 1 0 0 X 0 X^2+X 0 X^2 X^2 X^2 X^2 0 0 0 X X^2+X X^2+X X X X^2+X X^2+X X^2+X X^2+X X^2+X 0 X X^2+X X^2+X X^2+X X^2 0 X^2 0 X 0 X^2 X^2 X^2+X 0 X^2+X X^2+X 0 X^2+X X^2 X^2+X 0 X^2 X 0 X^2+X X^2 X^2+X X^2+X X^2 0 X^2+X X^2+X X X^2 X X^2+X X^2 X X^2 0 X^2 X X^2+X X^2+X 0 0 0 X^2 0 0 X X X X X^2 X 0 0 X X^2+X 0 0 0 0 X 0 0 0 X^2 X X^2+X X X^2+X X^2 X^2 X^2 X^2+X X X X X^2+X 0 X^2+X 0 X 0 X^2 X^2+X X X^2 X^2+X X^2+X X^2 X^2+X 0 X^2 0 X^2+X X^2 0 X^2 X X^2+X 0 X X X 0 X^2+X X^2 X^2 X X^2 X^2 X^2+X X^2+X X^2+X 0 X^2+X X X^2 0 X^2+X X 0 X X^2+X X 0 X 0 0 X^2+X X^2 X 0 X^2+X X^2 X^2+X X^2 X^2 X^2+X 0 X^2+X X^2+X X^2+X 0 0 0 0 X^2 0 0 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^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 0 X^2 X^2 0 X^2 X^2 0 0 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 0 0 0 0 0 0 X^2 0 0 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 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 0 0 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 0 X^2 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 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+273x^78+553x^80+672x^82+665x^84+565x^86+611x^88+449x^90+187x^92+44x^94+18x^96+31x^98+8x^100+10x^102+3x^104+4x^106+1x^112+1x^120 The gray image is a linear code over GF(2) with n=340, k=12 and d=156. This code was found by Heurico 1.16 in 5.56 seconds.