The generator matrix 1 0 1 1 1 X^2+X 1 1 0 1 1 X^2+X 0 1 1 X^2+X 1 1 0 1 1 X^2+X 1 1 0 1 1 1 X^2+X 1 1 X^2+X 0 1 1 1 0 1 1 X 1 1 1 1 0 X X^2+X X 1 1 X^2+X X X 1 0 1 X+1 X^2+X 1 1 0 X+1 1 X^2+X X^2+1 1 1 0 X^2+1 1 X^2+X X+1 1 X+1 0 1 X^2+1 X^2+X 1 0 X+1 X^2+1 1 X^2+X X+1 1 1 X+1 X^2+1 X+1 1 0 0 1 X^2+X X^2+1 X^2+X X^2+1 1 X 1 0 X X+1 1 X^2 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 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 X^2 0 0 X^2 X^2 0 X^2 0 0 0 X^2 0 X^2 X^2 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 X^2 0 X^2 0 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 0 X^2 0 0 X^2 0 0 0 0 0 0 X^2 0 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 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 0 0 0 X^2 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 0 0 0 0 0 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 0 0 X^2 X^2 X^2 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0 X^2 0 0 0 0 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 0 0 X^2 0 X^2 0 X^2 X^2 0 0 0 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 0 generates a code of length 54 over Z2[X]/(X^3) who´s minimum homogenous weight is 44. Homogenous weight enumerator: w(x)=1x^0+35x^44+46x^45+83x^46+174x^47+200x^48+436x^49+364x^50+788x^51+540x^52+1096x^53+646x^54+1136x^55+593x^56+804x^57+342x^58+428x^59+124x^60+170x^61+67x^62+34x^63+29x^64+8x^65+20x^66+12x^68+12x^70+1x^72+2x^74+1x^76 The gray image is a linear code over GF(2) with n=216, k=13 and d=88. This code was found by Heurico 1.16 in 3.15 seconds.