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 X X X X^2 0 X X 0 1 X 1 1 0 X^2 X X X 1 1 X 0 1 1 1 X 1 1 1 0 1 0 X 0 X 0 0 X X^2+X 0 0 X X^2+X X^2 0 X^2+X X^2+X X^2 X^2 X^2+X X X X X 0 X^2+X X X^2 X X X^2+X X^2+X 0 X X^2 X^2 X^2+X X X X^2+X X^2+X X X X X^2 X^2 X 0 0 X^2+X 0 X^2+X X^2 X^2 0 0 0 X X 0 X^2+X X 0 0 X^2+X X 0 X X^2 X 0 X^2 X 0 X^2 X X^2+X X 0 X^2 X X X 0 X^2 X^2 X X^2+X X X^2+X X^2 0 X^2+X 0 0 X X 0 X X X^2+X 0 X^2+X X^2+X X X^2 X X 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 0 0 0 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 X^2 0 0 X^2 0 0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 0 0 X^2 0 0 0 X^2 0 0 0 0 0 0 0 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 X^2 0 X^2 0 0 0 0 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 0 X^2 0 0 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 0 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 X^2 0 X^2 0 X^2 X^2 0 X^2 0 0 0 0 0 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 0 0 0 0 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 0 0 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 generates a code of length 54 over Z2[X]/(X^3) who´s minimum homogenous weight is 42. Homogenous weight enumerator: w(x)=1x^0+43x^42+68x^43+131x^44+150x^45+290x^46+376x^47+521x^48+656x^49+888x^50+1140x^51+1418x^52+1666x^53+1651x^54+1704x^55+1390x^56+1208x^57+929x^58+676x^59+487x^60+354x^61+240x^62+128x^63+116x^64+56x^65+38x^66+4x^67+28x^68+6x^69+11x^70+4x^72+6x^74 The gray image is a linear code over GF(2) with n=216, k=14 and d=84. This code was found by Heurico 1.16 in 15.9 seconds.