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 X^2 1 1 1 X 1 1 0 0 1 1 X 1 1 1 X 0 0 X 1 X 1 1 0 X 1 0 0 X 0 X 0 0 X X^2+X 0 X^2 X X^2+X 0 X^2+X X^2 X^2+X X 0 X^2 X X^2 X^2+X 0 X^2+X 0 X^2 X^2 X X 0 X X 0 X^2 X X^2+X 0 X^2 0 0 X X X X^2 X^2+X X^2 X^2+X X^2+X X^2+X 0 0 X^2 0 X^2+X 0 X^2 X^2 X X X X X^2+X X X^2 X^2 X X^2 0 X 0 0 X X 0 X^2+X X 0 X^2 X X 0 X^2 X^2+X X X^2 X 0 X^2+X 0 0 X^2 X^2+X X 0 0 X X X^2 X^2+X X^2+X X^2 0 X X 0 0 X^2+X X^2+X X^2 X X^2 X^2+X X^2 X^2 X 0 X^2 0 X X X^2+X X^2 X^2 X^2 X^2 X^2+X X^2+X 0 0 X 0 X^2+X 0 X^2 X^2 X X X^2 0 0 0 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 0 0 X^2 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 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 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 0 0 0 X^2 X^2 0 0 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 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 0 0 0 0 0 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 0 0 0 X^2 0 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+139x^62+12x^63+181x^64+44x^65+216x^66+108x^67+279x^68+172x^69+264x^70+132x^71+189x^72+36x^73+89x^74+4x^75+87x^76+4x^77+48x^78+24x^80+11x^82+6x^84+1x^86+1x^112 The gray image is a linear code over GF(2) with n=276, k=11 and d=124. This code was found by Heurico 1.16 in 31.7 seconds.