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 1 1 1 1 1 1 1 1 0 X^2 1 X 1 0 1 1 X 0 X^2 X 0 0 1 X^2 X X^2 X^2 1 0 1 0 X 0 0 0 0 0 0 0 X X^2+X X X X^2+X X X^2 X X^2 X^2+X X^2 0 X^2 0 X X^2+X X X^2 X^2+X 0 X X X X^2 X^2+X 0 X X X^2 X^2 0 X X X^2 X^2 0 X^2 0 0 X 0 X^2 0 X X^2 X^2 X^2 X^2 0 0 X 0 0 0 X X^2+X X 0 0 0 X X X^2+X X^2 X X^2+X X^2 X X^2+X X^2 X^2 X^2 X 0 X^2+X 0 X^2 0 X^2 X X X X 0 X^2 X 0 X^2 X^2+X X^2+X X X^2+X 0 X X^2 X^2 0 0 X X X X X^2+X X^2 0 0 0 0 X 0 X X X^2+X 0 X X X^2 0 X^2 X^2+X X X^2+X X^2+X X^2+X 0 X X X^2 0 X 0 X^2 X^2+X X^2 X^2+X X^2 X^2+X X^2+X 0 X^2+X X^2 X^2 X^2 X^2 X X^2 X^2 0 0 X^2 X^2+X X^2+X X X X X^2 X^2+X X^2+X 0 X^2+X X X^2+X 0 0 0 0 X X 0 X^2+X X X^2 X^2+X X^2+X 0 X^2+X X X^2 0 X X^2 X 0 X X^2+X X^2+X X X^2 X^2 X 0 X^2 X^2 X X 0 X^2 0 X X X^2+X X X^2+X X X X^2+X X 0 X X^2 X^2+X X^2 X^2 0 X X^2 X 0 X 0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 0 0 X^2 0 X^2 0 X^2 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2 0 X^2 0 0 0 0 X^2 X^2 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 0 X^2 0 0 X^2 0 generates a code of length 57 over Z2[X]/(X^3) who´s minimum homogenous weight is 46. Homogenous weight enumerator: w(x)=1x^0+61x^46+144x^47+206x^48+292x^49+400x^50+528x^51+599x^52+882x^53+1189x^54+1358x^55+1571x^56+1760x^57+1860x^58+1422x^59+1031x^60+890x^61+633x^62+530x^63+358x^64+210x^65+178x^66+106x^67+64x^68+60x^69+29x^70+8x^71+7x^72+2x^73+2x^74+1x^76+1x^80+1x^84 The gray image is a linear code over GF(2) with n=228, k=14 and d=92. This code was found by Heurico 1.16 in 16.8 seconds.