The generator matrix 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 0 1 1 X 1 0 X 0 1 X 1 1 0 1 X X 1 1 1 1 0 1 0 1 1 1 X^2 1 X^2 X X X 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 0 X^2+X X X^2+X 0 X^2+X X^2+X X X^2+X X 0 X^2+X X^2 X^2+X X X X^2+X X^2+X 0 0 X^2+X 0 X X^2 X X X X^2 X^2 X^2+X 0 X^2+X 0 0 0 0 X^2 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 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 0 X^2 0 0 0 0 0 X^2 0 0 0 0 0 0 0 X^2 0 0 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 X^2 X^2 0 0 X^2 0 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 0 X^2 0 0 X^2 0 0 0 0 0 X^2 0 0 0 0 0 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 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 0 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 X^2 0 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 0 X^2 0 0 0 0 0 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 0 0 0 0 0 X^2 X^2 0 0 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 0 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 0 0 X^2 0 0 X^2 0 0 X^2 X^2 0 0 X^2 0 X^2 0 X^2 0 0 0 generates a code of length 47 over Z2[X]/(X^3) who´s minimum homogenous weight is 34. Homogenous weight enumerator: w(x)=1x^0+43x^34+150x^36+278x^38+16x^39+550x^40+128x^41+1067x^42+448x^43+1746x^44+896x^45+2313x^46+1120x^47+2335x^48+896x^49+1766x^50+448x^51+1017x^52+128x^53+536x^54+16x^55+292x^56+115x^58+44x^60+25x^62+6x^64+1x^66+3x^68 The gray image is a linear code over GF(2) with n=188, k=14 and d=68. This code was found by Heurico 1.16 in 13.3 seconds.