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 X X X 1 1 X X X X X^2 1 X X 1 1 X X 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 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 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 X^2 0 0 0 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 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 0 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 0 X^2 X^2 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 X^2 0 X^2 X^2 X^2 0 0 X^2 0 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 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 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 0 0 X^2 0 0 X^2 0 X^2 0 0 X^2 0 0 X^2 X^2 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 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 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 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 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 0 X^2 0 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 0 generates a code of length 50 over Z2[X]/(X^3) who´s minimum homogenous weight is 40. Homogenous weight enumerator: w(x)=1x^0+136x^40+16x^42+267x^44+128x^46+393x^48+1024x^49+224x^50+1024x^51+365x^52+128x^54+218x^56+16x^58+114x^60+36x^64+5x^68+1x^76 The gray image is a linear code over GF(2) with n=200, k=12 and d=80. This code was found by Heurico 1.16 in 1.27 seconds.