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 X 0 X X^2 X X 1 X 0 1 X^2 1 1 1 0 X 1 X 1 1 0 X^2 X 1 1 1 1 X X 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^2 X X^2 0 X X X^2+X X X 0 X X X 0 X^2+X 0 0 X^2+X X 0 X^2+X X X X X^2 X^2 X^2 X X^2 X 0 0 0 0 X X 0 X^2+X X 0 0 X^2+X X 0 X X^2 X 0 X X^2 0 X X^2 0 X X X X 0 X X^2+X X^2+X X^2 X X^2+X X^2+X X 0 X X^2 X^2 X^2+X X X^2 0 X X 0 X^2+X X^2 X^2 X X^2 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 0 X^2 0 0 0 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 0 0 X^2 X^2 0 X^2 X^2 0 X^2 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 0 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 0 0 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 0 0 X^2 0 X^2 X^2 0 0 0 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 0 0 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 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 0 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 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 X^2 0 0 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 0 0 X^2 0 X^2 0 X^2 0 0 0 0 X^2 0 0 X^2 0 0 X^2 0 0 generates a code of length 52 over Z2[X]/(X^3) who´s minimum homogenous weight is 40. Homogenous weight enumerator: w(x)=1x^0+88x^40+36x^41+184x^42+160x^43+221x^44+374x^45+304x^46+814x^47+443x^48+2036x^49+547x^50+2692x^51+549x^52+2732x^53+509x^54+2076x^55+434x^56+844x^57+358x^58+360x^59+228x^60+110x^61+122x^62+38x^63+70x^64+12x^65+15x^66+4x^67+9x^68+9x^70+4x^72+1x^76 The gray image is a linear code over GF(2) with n=208, k=14 and d=80. This code was found by Heurico 1.16 in 14.6 seconds.