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 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 1 X 1 1 1 X X 1 1 1 X 1 1 0 X^2 0 0 0 0 0 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2 0 X^2 X^2 0 0 0 0 0 0 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 0 X^2 0 0 X^2 0 X^2 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 X^2 0 0 0 0 0 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 0 0 0 X^2 X^2 0 X^2 0 X^2 0 0 0 X^2 0 0 0 X^2 0 0 0 0 X^2 0 0 X^2 0 X^2 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 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 X^2 X^2 0 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 0 0 0 0 X^2 0 0 0 X^2 0 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 0 0 0 X^2 0 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 0 0 X^2 0 X^2 0 X^2 0 X^2 0 0 X^2 0 X^2 0 0 0 0 0 X^2 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 0 0 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 X^2 X^2 0 0 0 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 0 0 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 0 0 X^2 X^2 0 X^2 X^2 0 0 0 0 X^2 0 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 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 0 0 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 0 0 X^2 0 0 0 X^2 X^2 0 0 0 X^2 X^2 0 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 generates a code of length 69 over Z2[X]/(X^3) who´s minimum homogenous weight is 62. Homogenous weight enumerator: w(x)=1x^0+50x^62+70x^64+40x^66+80x^68+512x^69+126x^70+88x^72+8x^74+30x^78+16x^80+2x^86+1x^128 The gray image is a linear code over GF(2) with n=276, k=10 and d=124. This code was found by Heurico 1.16 in 2.04 seconds.