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 1 1 1 1 1 X 1 1 1 1 1 1 0 1 1 1 1 1 X 1 1 X X X^2 1 0 1 1 1 X 1 X^2 1 1 0 X 0 X^2+X 0 X^2+X 0 X^2+X X^2 X^2+X 0 X^2+X X 0 X^2 X^2+X X^2 X^2+X X^2 X 0 0 X^2+X X 0 X^2 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 X X^2+X 0 X^2+X X^2+X 0 X X^2+X X X^2+X X^2 X X^2 X^2 X^2+X X^2 X^2 X^2+X 0 X^2 X^2 X X X X^2 X^2 X^2+X 0 X^2 X^2+X 0 0 X^2 0 0 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 0 0 0 X^2 X^2 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 0 0 0 0 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 0 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 0 0 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 0 X^2 0 0 0 0 0 0 X^2 0 0 0 0 0 X^2 0 0 0 X^2 0 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 0 0 0 0 0 X^2 0 0 0 X^2 0 0 X^2 0 0 X^2 0 X^2 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 0 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 0 0 0 0 0 0 0 X^2 0 X^2 0 X^2 0 0 0 X^2 0 0 0 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 0 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 0 X^2 0 0 X^2 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 0 0 0 0 X^2 X^2 0 X^2 0 0 0 0 X^2 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 0 0 0 X^2 0 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 0 X^2 X^2 generates a code of length 69 over Z2[X]/(X^3) who´s minimum homogenous weight is 61. Homogenous weight enumerator: w(x)=1x^0+90x^61+51x^62+103x^64+170x^65+124x^66+128x^67+220x^68+276x^69+273x^70+128x^71+164x^72+132x^73+36x^74+4x^76+82x^77+25x^78+16x^80+18x^81+3x^86+3x^88+1x^120 The gray image is a linear code over GF(2) with n=276, k=11 and d=122. This code was found by Heurico 1.16 in 12.1 seconds.