The generator matrix 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 0 1 1 X 0 X 1 1 0 1 1 X 0 1 X 1 1 0 1 X 0 1 0 1 X 0 1 X 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+X 0 X X^2+X 0 X^2+X X X^2+X X^2+X 0 X X^2 X^2+X X^2+X X X^2+X X^2+X X^2 X^2 X X X^2+X X X^2+X X 0 0 X 0 0 X^2+X 0 0 X^2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 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 X^2 0 0 X^2 0 X^2 0 X^2 X^2 0 X^2 0 0 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 0 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 0 0 0 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 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 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 0 0 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 X^2 X^2 0 0 X^2 0 X^2 0 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 0 X^2 0 0 0 0 0 0 0 X^2 0 X^2 0 0 X^2 0 X^2 X^2 0 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0 0 X^2 X^2 0 X^2 X^2 0 0 X^2 0 X^2 0 X^2 X^2 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 0 0 X^2 X^2 0 X^2 generates a code of length 44 over Z2[X]/(X^3) who´s minimum homogenous weight is 32. Homogenous weight enumerator: w(x)=1x^0+130x^32+44x^34+501x^36+624x^38+1956x^40+2936x^42+4005x^44+2880x^46+2056x^48+636x^50+431x^52+48x^54+108x^56+23x^60+5x^64 The gray image is a linear code over GF(2) with n=176, k=14 and d=64. This code was found by Heurico 1.16 in 12.3 seconds.