The generator matrix 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 0 X 0 1 1 1 1 X 0 1 1 1 X 1 1 1 1 0 1 1 1 0 1 1 1 1 X X X 1 1 0 X 0 X^2+X 0 X^2+X 0 X^2+X 0 X^2+X X^2 X^2+X 0 X^2+X X 0 X^2 0 0 X^2 X^2+X X X^2+X X X^2+X X^2+X X X^2+X X^2+X X 0 X^2+X X^2 X^2+X 0 X X^2 0 X 0 0 X^2+X X X X^2+X X X^2+X X^2+X X^2+X X^2+X X^2 0 0 0 X^2 0 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 0 0 0 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 0 0 0 X^2 X^2 0 X^2 X^2 0 0 0 0 X^2 0 0 0 0 0 0 0 X^2 0 X^2 X^2 0 0 0 0 0 0 X^2 X^2 0 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 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 0 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 0 0 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 X^2 0 0 0 X^2 0 X^2 0 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 0 X^2 0 0 0 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 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 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 X^2 0 0 X^2 X^2 0 X^2 0 0 0 0 0 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 0 X^2 X^2 X^2 X^2 X^2 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 X^2 0 0 X^2 0 X^2 0 X^2 X^2 0 0 0 0 X^2 0 X^2 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 0 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 0 0 0 X^2 0 generates a code of length 52 over Z2[X]/(X^3) who´s minimum homogenous weight is 42. Homogenous weight enumerator: w(x)=1x^0+26x^42+12x^43+65x^44+120x^45+96x^46+180x^47+117x^48+476x^49+145x^50+748x^51+173x^52+748x^53+135x^54+476x^55+88x^56+180x^57+76x^58+120x^59+43x^60+12x^61+22x^62+17x^64+9x^66+7x^68+3x^70+1x^80 The gray image is a linear code over GF(2) with n=208, k=12 and d=84. This code was found by Heurico 1.16 in 1.08 seconds.