The generator matrix 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 X^2 X^2 X 1 X 1 X^2 X 0 1 0 1 X 1 1 X^2 0 X X^2 X^2 X 1 X 1 1 0 0 X 0 0 0 X X^2+X X 0 X^2 X^2 X X^2+X 0 X^2+X X X^2 X^2 X^2+X 0 X^2 X X^2 X X 0 X 0 0 X X^2+X 0 X^2+X X^2+X X X X X^2+X 0 X X^2+X 0 X^2+X X^2 0 X X^2 X X^2+X X^2+X 0 X^2+X X X 0 0 X 0 X X X^2+X 0 0 0 X X^2 X X^2+X X^2 X X^2 0 X^2+X X X X^2 0 X 0 X^2+X X 0 X X^2 0 X X^2 X X X 0 X^2 X^2 X X^2+X X^2+X X^2 0 X X^2 X X^2 X X X X^2+X X^2 X 0 0 0 X X 0 X^2+X X 0 X 0 X X^2+X X^2+X X^2 X^2 0 X^2+X X X^2+X X^2 0 X^2+X X^2+X X 0 X^2 X X^2+X X^2+X X^2 X^2 X^2 0 0 0 X^2 X^2 X 0 0 0 X^2+X X X^2 X 0 X 0 X^2 X^2 X^2+X X^2+X X^2+X 0 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 0 0 X^2 0 0 X^2 0 0 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 X^2 0 0 0 X^2 0 X^2 0 0 X^2 X^2 0 0 X^2 0 X^2 0 0 X^2 X^2 0 0 0 0 0 0 X^2 0 0 0 X^2 0 0 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 0 0 0 0 0 X^2 0 0 0 0 X^2 X^2 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 X^2 0 0 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 0 X^2 0 0 X^2 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 0 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 generates a code of length 54 over Z2[X]/(X^3) who´s minimum homogenous weight is 43. Homogenous weight enumerator: w(x)=1x^0+76x^43+134x^44+180x^45+292x^46+344x^47+570x^48+694x^49+937x^50+1196x^51+1348x^52+1624x^53+1587x^54+1584x^55+1439x^56+1180x^57+984x^58+724x^59+498x^60+356x^61+244x^62+152x^63+91x^64+62x^65+37x^66+20x^67+12x^68+12x^70+3x^72+2x^74+1x^86 The gray image is a linear code over GF(2) with n=216, k=14 and d=86. This code was found by Heurico 1.16 in 25 seconds.