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 0 X 1 1 X X 1 1 X^2 1 1 1 1 0 1 1 X X^2 X^2 1 0 1 1 1 1 1 1 X^2 1 X 1 1 X 1 X^2 X^2 1 1 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 0 0 X X^2+X 0 X^2+X X^2+X X^2 0 X 0 X^2 X^2+X X^2+X X X 0 X X X X 0 X^2 X^2+X 0 X^2+X X^2+X X X X X 0 X^2+X X X X X^2 X 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 X^2+X X X^2+X X^2+X X 0 0 X^2+X X^2 X^2+X 0 X 0 X^2 0 0 X^2 X^2+X X^2+X X X^2+X X X^2 X X^2 X^2 X^2 X X^2+X X^2+X 0 0 X^2+X X^2 0 X^2+X X 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 0 0 X^2 0 0 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 0 0 0 X^2 X^2 0 0 X^2 X^2 X^2 0 0 X^2 0 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 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 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 X^2 0 0 X^2 0 0 X^2 X^2 0 0 0 X^2 X^2 0 0 0 0 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 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 0 0 X^2 0 0 0 0 X^2 X^2 0 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 0 X^2 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 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 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 0 X^2 0 0 generates a code of length 66 over Z2[X]/(X^3) who´s minimum homogenous weight is 56. Homogenous weight enumerator: w(x)=1x^0+23x^56+50x^57+68x^58+138x^59+146x^60+210x^61+238x^62+274x^63+360x^64+372x^65+449x^66+364x^67+371x^68+278x^69+168x^70+180x^71+73x^72+90x^73+74x^74+58x^75+38x^76+22x^77+18x^78+10x^79+7x^80+9x^82+4x^84+2x^85+1x^100 The gray image is a linear code over GF(2) with n=264, k=12 and d=112. This code was found by Heurico 1.16 in 1.4 seconds.