The generator matrix 1 1 1 1 1 1 1 1 1 1 1 1 X 1 0 1 1 X 1 0 X 1 0 1 1 1 X X 1 1 0 1 1 1 1 X^2 0 X 0 1 X X 1 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 X^2+X X 0 X^2+X X^2+X 0 X X^2+X 0 X X^2+X X X^2 X^2+X X^2+X X^2 X^2+X X X^2 X^2+X 0 0 0 X X^2+X X X^2+X X^2+X X^2 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 0 0 0 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 X^2 0 X^2 0 0 0 X^2 0 0 0 0 0 0 0 X^2 0 0 X^2 0 X^2 0 X^2 0 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 X^2 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 0 X^2 0 X^2 0 X^2 0 0 0 X^2 0 0 X^2 X^2 0 X^2 0 X^2 0 0 0 0 0 X^2 0 0 0 0 0 X^2 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 X^2 0 0 0 X^2 X^2 0 0 0 0 X^2 X^2 0 0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 X^2 X^2 0 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 X^2 0 0 X^2 0 X^2 0 0 X^2 0 X^2 X^2 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 0 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 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 0 X^2 X^2 X^2 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 generates a code of length 43 over Z2[X]/(X^3) who´s minimum homogenous weight is 32. Homogenous weight enumerator: w(x)=1x^0+205x^32+104x^34+16x^35+655x^36+128x^37+776x^38+448x^39+1943x^40+896x^41+2336x^42+1120x^43+2768x^44+896x^45+1568x^46+448x^47+1207x^48+128x^49+312x^50+16x^51+308x^52+24x^54+65x^56+12x^60+3x^64+1x^68 The gray image is a linear code over GF(2) with n=172, k=14 and d=64. This code was found by Heurico 1.16 in 84.2 seconds.