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 X 0 1 1 1 1 1 1 X 1 1 0 0 X X 0 X 1 1 0 1 X 1 1 1 0 1 0 X 1 0 1 1 1 X^2 X 1 X^2 1 1 0 1 1 1 1 0 X 0 X^2+X 0 X^2+X 0 X^2+X 0 X^2+X 0 X^2+X X^2+X X^2 0 X^2+X X X^2 X^2+X X^2+X X 0 0 X^2 X^2+X X 0 0 X^2+X X^2+X 0 X^2 X^2+X X^2+X X X X X^2+X X^2+X X X^2+X 0 X^2+X X X^2 X^2+X X X^2 X^2+X X X X X^2+X 0 X X^2+X 0 X 0 X^2 X 0 0 X^2 X X^2+X 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 X^2 0 X^2 0 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 X^2 X^2 X^2 0 0 0 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 X^2 0 0 X^2 0 X^2 X^2 X^2 0 0 X^2 0 0 X^2 0 X^2 X^2 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 X^2 0 0 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 0 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 0 0 X^2 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 0 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 0 X^2 0 0 X^2 0 X^2 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 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 X^2 0 X^2 X^2 0 0 0 X^2 X^2 0 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 0 0 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 0 X^2 X^2 0 0 X^2 X^2 0 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 0 X^2 0 0 0 0 0 X^2 0 0 X^2 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 X^2 0 0 X^2 0 0 0 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 0 0 0 X^2 0 0 0 0 0 X^2 X^2 0 X^2 X^2 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0 X^2 0 0 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 0 0 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 0 X^2 0 0 0 0 0 0 0 0 0 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 0 0 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 0 X^2 X^2 0 X^2 X^2 0 0 0 X^2 0 0 X^2 0 0 X^2 generates a code of length 69 over Z2[X]/(X^3) who´s minimum homogenous weight is 56. Homogenous weight enumerator: w(x)=1x^0+189x^56+86x^58+573x^60+648x^62+1510x^64+2094x^66+3243x^68+2768x^70+2435x^72+1314x^74+858x^76+232x^78+281x^80+26x^82+88x^84+32x^88+5x^92+1x^100 The gray image is a linear code over GF(2) with n=276, k=14 and d=112. This code was found by Heurico 1.16 in 99.8 seconds.