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 X 0 X X X X 0 X^2 0 X X X^2 X 1 1 X 1 1 1 X 0 1 0 X^2 0 0 1 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 X^2 X^2 X^2+X X X^2+X X^2 X 0 X X^2 0 X^2+X 0 X X X X^2 0 0 0 X^2 X X X X X^2 X X^2 X^2 X X^2+X X X X X X^2 0 0 X 0 X X X^2+X 0 0 0 X X^2 X X^2+X X^2 X X^2+X 0 X^2+X X^2+X 0 0 0 X^2 X X X^2 X X^2+X X X^2+X X^2 0 X X X^2+X X X X^2+X 0 X^2+X X^2 X^2+X X^2+X X^2 X 0 X X^2 X^2+X X X^2+X 0 0 0 0 X X 0 X^2+X X 0 X 0 X X^2+X X^2+X X^2 X^2 X 0 X 0 0 X^2 X X^2+X X^2 X^2+X X^2+X X^2 X^2+X X 0 X X^2 X^2+X 0 0 X^2+X X^2+X 0 X^2+X X X^2 X^2 X^2+X X X^2+X X^2+X X^2 0 X^2+X X X^2+X 0 0 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 0 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 0 X^2 0 X^2 X^2 0 0 0 X^2 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 0 0 X^2 0 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 0 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 0 0 X^2 0 0 X^2 X^2 X^2 0 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 0 X^2 0 X^2 0 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 X^2 0 0 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0 0 X^2 0 X^2 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 X^2 0 X^2 X^2 0 X^2 0 generates a code of length 53 over Z2[X]/(X^3) who´s minimum homogenous weight is 42. Homogenous weight enumerator: w(x)=1x^0+53x^42+116x^43+264x^44+262x^45+375x^46+542x^47+775x^48+1032x^49+1032x^50+1342x^51+1592x^52+1490x^53+1562x^54+1522x^55+1195x^56+1036x^57+629x^58+492x^59+440x^60+246x^61+158x^62+78x^63+76x^64+28x^65+30x^66+2x^67+8x^68+2x^69+2x^71+1x^72+1x^94 The gray image is a linear code over GF(2) with n=212, k=14 and d=84. This code was found by Heurico 1.16 in 15.1 seconds.