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 X X X^2 1 X X^2 1 0 1 1 1 X^2 1 X 1 1 1 1 X 1 X 1 X 0 1 1 X 1 X 0 0 X^2 X X 0 X 0 X 0 0 X X^2+X 0 X^2 X^2+X X 0 X X X^2 X^2 X^2+X 0 X X^2+X 0 X X^2 X X X^2 X^2+X X X X^2+X X^2+X X X^2+X X X^2+X 0 0 X X X^2 X X X^2 0 X X 0 0 X 0 X 0 X X^2 0 X X^2 X 0 0 0 0 X X 0 X^2+X X 0 X^2 X 0 X 0 X^2+X X^2 X X X^2 0 X^2+X X^2+X X X^2 0 X^2 X X 0 X X X^2+X 0 X^2+X 0 0 0 X^2 X^2 X^2+X 0 X X X X^2+X 0 X X X^2+X X^2+X X^2+X X X^2+X X^2 X^2+X X X X^2 X X X^2+X 0 0 0 0 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 0 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 X^2 0 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 X^2 X^2 0 0 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 0 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 X^2 X^2 0 0 0 0 X^2 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 0 0 0 0 X^2 X^2 X^2 0 0 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 0 0 0 0 X^2 X^2 0 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 0 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 X^2 X^2 0 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 generates a code of length 61 over Z2[X]/(X^3) who´s minimum homogenous weight is 52. Homogenous weight enumerator: w(x)=1x^0+83x^52+8x^53+205x^54+96x^55+267x^56+232x^57+275x^58+400x^59+256x^60+552x^61+218x^62+448x^63+229x^64+216x^65+217x^66+80x^67+134x^68+16x^69+87x^70+45x^72+19x^74+6x^76+2x^78+2x^80+1x^82+1x^84 The gray image is a linear code over GF(2) with n=244, k=12 and d=104. This code was found by Heurico 1.16 in 1.25 seconds.