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 0 X 0 0 1 X 1 X 1 1 0 1 1 1 1 X 0 1 1 X 0 1 1 X 0 1 1 1 X^2 1 1 1 0 X 1 0 1 0 1 1 X 0 X 0 X^2+X 0 X^2+X 0 X^2+X 0 X^2+X 0 X^2+X X^2+X X^2 0 X^2+X X X^2 X^2+X 0 X^2+X 0 X^2 X X^2+X X X^2+X X X 0 X^2+X 0 X^2+X X^2+X X^2+X X X^2 X^2+X X^2+X X^2 X^2+X X 0 X^2+X X^2+X X X X^2 X^2+X X X X X^2+X 0 0 X^2 0 X X^2+X X^2 X X^2 X X^2+X 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 0 X^2 0 0 X^2 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 X^2 0 X^2 0 0 0 0 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 0 X^2 0 0 0 X^2 X^2 0 X^2 0 0 X^2 0 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 X^2 0 0 X^2 0 X^2 0 X^2 X^2 0 X^2 0 0 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 X^2 0 0 X^2 0 0 0 X^2 X^2 X^2 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 0 0 X^2 0 0 0 0 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 0 X^2 0 X^2 X^2 0 0 0 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 0 X^2 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 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 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 0 0 0 X^2 0 X^2 0 X^2 0 0 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 X^2 0 0 X^2 0 X^2 0 X^2 X^2 0 X^2 0 0 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 0 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 0 X^2 0 0 X^2 0 0 0 0 0 0 0 0 0 0 0 X^2 0 X^2 0 0 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 0 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 X^2 0 X^2 X^2 0 X^2 0 0 X^2 0 X^2 0 0 X^2 0 X^2 0 0 0 0 0 0 0 0 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 X^2 0 0 0 X^2 0 0 0 0 0 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 0 0 X^2 0 0 X^2 0 X^2 0 0 generates a code of length 66 over Z2[X]/(X^3) who´s minimum homogenous weight is 52. Homogenous weight enumerator: w(x)=1x^0+109x^52+38x^54+412x^56+40x^57+296x^58+176x^59+829x^60+584x^61+678x^62+1376x^63+1232x^64+1968x^65+1024x^66+1856x^67+1239x^68+1328x^69+722x^70+672x^71+793x^72+168x^73+280x^74+16x^75+347x^76+8x^77+34x^78+115x^80+32x^84+7x^88+4x^92 The gray image is a linear code over GF(2) with n=264, k=14 and d=104. This code was found by Heurico 1.16 in 23.6 seconds.