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 X X^2 X^2 X^2 X^2 1 X 0 X 1 X^2 1 1 0 X X 1 X 1 1 1 1 0 X X 1 X^2 1 1 0 X 0 0 0 X X^2+X X 0 X^2 X^2 X X^2+X X X 0 0 0 X^2 X^2+X X^2+X X^2 X^2+X X X^2+X 0 0 X^2+X X 0 X X^2 X X X X X X 0 X^2 X X^2+X X X X^2 X^2+X 0 X^2+X X^2+X X^2+X X^2 0 X^2+X X X^2 0 X X^2 0 X^2 X^2+X X 0 0 X 0 X X X^2+X 0 0 0 X X X 0 X^2 X^2+X X 0 X^2 X^2 0 0 X^2+X X^2 X X^2+X X^2 X^2+X 0 X^2+X X X^2+X X 0 X X X^2+X X^2 X X X^2 X^2 X^2 0 0 X^2+X X X 0 X^2+X X X^2+X X^2 0 0 0 X^2+X X 0 X^2 0 0 0 0 0 X X 0 X^2+X X X^2 X X^2 0 X X^2 X^2+X X X^2 X^2 X X^2+X X^2 X 0 X X^2+X X^2+X 0 X^2+X 0 0 0 X^2+X X^2+X X^2+X 0 0 X^2 X^2+X 0 X^2 0 X^2+X X^2+X X X^2 X^2 X^2 X^2+X 0 X 0 X X X X X X^2+X 0 X^2 X X X 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 X^2 X^2 0 X^2 X^2 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 0 0 0 X^2 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 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 0 0 X^2 X^2 0 0 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 0 0 0 0 0 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 0 0 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 0 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 X^2 0 0 X^2 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 0 X^2 X^2 0 X^2 0 0 0 X^2 0 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 0 0 0 X^2 0 0 generates a code of length 62 over Z2[X]/(X^3) who´s minimum homogenous weight is 52. Homogenous weight enumerator: w(x)=1x^0+90x^52+90x^53+181x^54+220x^55+260x^56+442x^57+380x^58+616x^59+701x^60+702x^61+912x^62+710x^63+688x^64+622x^65+396x^66+406x^67+216x^68+136x^69+145x^70+86x^71+74x^72+48x^73+21x^74+10x^75+17x^76+8x^77+10x^78+1x^80+2x^82+1x^90 The gray image is a linear code over GF(2) with n=248, k=13 and d=104. This code was found by Heurico 1.16 in 5.35 seconds.