The generator matrix 1 0 0 1 1 1 X^2+X X 1 1 1 X^2 X^2 1 0 1 1 1 0 1 X^2 1 1 X X^2+X 1 X 1 1 1 X^2 1 X^2 1 X 1 X^2+X X^2+X 1 1 1 1 0 X 1 0 X^2 1 1 0 X 0 0 X 1 1 X^2 1 1 X^2+X X^2 1 X X^2+X X 1 1 X^2 1 1 1 1 1 1 0 1 1 X^2+X 1 X^2 1 1 1 X^2+X 1 X 1 1 1 1 0 1 0 0 1 X+1 1 X^2 X^2+X+1 X+1 X^2+X 1 1 X^2 0 0 X X^2+X+1 1 X^2+X+1 1 X^2 1 1 0 X^2+X 1 X X^2+X+1 X^2 1 X^2+X+1 1 1 X^2+X X^2+X X^2+X 1 X^2+X X X^2 1 1 1 X^2 1 1 X+1 X^2+1 X 1 1 1 X X^2+1 X^2+1 1 X+1 1 1 1 0 1 X 1 X^2 X^2+1 X^2 X X^2+X X+1 X^2+1 0 X+1 1 X^2+X X^2 1 X^2+X 0 X^2+1 X+1 X^2 1 X^2 X X^2+1 X^2+1 X^2+X+1 X^2+X 0 0 1 1 1 X^2 1 1 X+1 X^2+X X^2+1 X^2+1 X^2+X X 1 X^2+X+1 X X^2+X+1 X^2+X+1 0 X^2+X 1 1 X^2+1 1 X^2+X X X+1 X X^2 0 X^2 X^2+1 X^2+X+1 1 X^2+X+1 1 X^2+X+1 1 X^2 X X^2+X+1 X+1 0 0 X^2+1 0 X^2+X X^2+1 1 X^2+X X+1 X^2 1 0 0 X^2+X X^2+X 1 X^2+1 X^2+X+1 1 X+1 1 X^2+X+1 X^2 X^2+X 1 X^2+X+1 X^2 X+1 1 X^2+X+1 0 X+1 X^2+1 X^2+X X^2+1 X^2 1 X^2 X^2 X^2+1 1 X 1 X+1 X^2+X X+1 X^2+X 0 0 0 X X^2+X 0 X X X^2+X 0 X^2+X X^2+X 0 0 X^2+X X^2+X X^2 0 0 X^2+X X X^2 0 X^2 X^2 X X^2+X 0 X X X^2 X^2 X^2+X X^2+X X X X^2+X X^2 X^2 X^2 X 0 X X^2+X X^2+X X X X^2 X X^2 0 0 X^2+X 0 0 X 0 X^2+X X^2+X X X^2+X X^2 X X^2 0 X^2+X 0 X^2+X X^2 X^2+X X X^2 X X^2+X 0 X^2 X^2 0 X^2 X^2 0 X 0 0 X 0 X X X X 0 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 0 X^2 0 0 X^2 X^2 0 X^2 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 0 0 0 0 X^2 0 X^2 0 0 X^2 0 0 X^2 generates a code of length 90 over Z2[X]/(X^3) who´s minimum homogenous weight is 84. Homogenous weight enumerator: w(x)=1x^0+452x^84+668x^86+926x^88+576x^90+612x^92+236x^94+282x^96+140x^98+114x^100+40x^102+38x^104+4x^106+6x^108+1x^112 The gray image is a linear code over GF(2) with n=360, k=12 and d=168. This code was found by Heurico 1.16 in 7.72 seconds.