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 X X X X X 1 1 X 1 X 1 1 1 X X 1 1 X 1 1 0 X^2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 0 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 X^2 0 0 0 0 0 0 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 X^2 X^2 0 X^2 0 X^2 0 0 X^2 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 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 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 0 0 0 X^2 0 0 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 0 X^2 X^2 0 0 0 X^2 X^2 0 0 0 X^2 0 X^2 X^2 0 0 X^2 0 0 0 0 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 0 0 0 X^2 X^2 0 0 X^2 0 0 X^2 X^2 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 0 0 X^2 X^2 0 X^2 0 X^2 0 0 0 0 0 0 0 0 0 X^2 0 0 X^2 0 0 X^2 0 0 X^2 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 X^2 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 X^2 X^2 X^2 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 0 X^2 0 X^2 0 X^2 X^2 0 X^2 0 0 X^2 X^2 0 X^2 0 0 0 0 0 0 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 X^2 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 0 X^2 0 X^2 X^2 0 0 generates a code of length 52 over Z2[X]/(X^3) who´s minimum homogenous weight is 40. Homogenous weight enumerator: w(x)=1x^0+76x^40+177x^44+42x^46+291x^48+224x^50+2502x^52+196x^54+313x^56+48x^58+131x^60+2x^62+68x^64+21x^68+3x^72+1x^84 The gray image is a linear code over GF(2) with n=208, k=12 and d=80. This code was found by Heurico 1.16 in 1.26 seconds.