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 X^2 X X 1 0 X^2 X X^2 1 X^2 X^2 0 X 1 X^2 1 0 1 1 0 1 1 1 X^2 X 1 1 X^2 1 X^2 0 X 0 0 0 X X^2+X X 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^2+X X X^2+X 0 0 X^2+X X 0 X X^2 X X^2 X X X X^2 0 X 0 X X^2 X X^2 X 0 0 X X X X X^2+X 0 0 X^2 0 X X^2+X X^2+X 0 X^2 0 X^2 0 0 X 0 X X X^2+X 0 0 0 X X X 0 X^2 X^2+X X 0 X^2 X^2 0 0 X^2+X X^2 X X^2+X X^2 X^2+X 0 X^2+X X X^2+X X X X X^2+X 0 X^2 X X^2 X^2+X X^2+X 0 X^2+X X X^2 X X^2 X^2 X X X^2+X X^2+X X X^2 X^2 0 X^2+X X^2+X 0 X^2+X X X^2+X X^2 0 0 0 X X 0 X^2+X X X^2 X X^2 0 X X^2 X^2+X X X^2 X^2 X X^2+X X^2 X 0 X X^2+X X^2+X 0 X^2+X 0 0 0 X^2+X X^2+X X^2 0 0 X^2+X 0 0 X^2+X 0 X^2 X 0 X^2+X 0 X^2 X X^2+X 0 X X^2 0 0 X^2 X^2 X^2+X 0 0 X 0 X X X^2 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 0 X^2 0 X^2 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 0 0 0 0 0 X^2 0 0 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 0 0 X^2 X^2 0 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 0 0 0 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 X^2 0 0 X^2 X^2 0 0 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 0 0 0 0 X^2 0 0 X^2 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 0 X^2 X^2 X^2 generates a code of length 64 over Z2[X]/(X^3) who´s minimum homogenous weight is 54. Homogenous weight enumerator: w(x)=1x^0+124x^54+12x^55+351x^56+44x^57+468x^58+148x^59+746x^60+384x^61+947x^62+460x^63+1022x^64+388x^65+934x^66+380x^67+622x^68+204x^69+422x^70+24x^71+257x^72+140x^74+63x^76+4x^77+35x^78+9x^80+2x^82+1x^92 The gray image is a linear code over GF(2) with n=256, k=13 and d=108. This code was found by Heurico 1.16 in 5.65 seconds.