The generator matrix 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X X 1 0 X^2 1 0 X 1 1 1 1 1 X 0 0 1 X 1 X X 1 1 X 1 X^2 X X 1 0 X 0 X 0 0 X X^2+X 0 0 X X^2+X X^2 X^2+X X 0 X^2+X X X^2 X 0 X X^2 X X X X X^2+X X^2 X^2 X^2 X^2 X^2 X^2 X^2+X X^2+X X^2+X X^2+X X^2 X^2 X X^2 X X X 0 0 0 X X 0 X^2+X X 0 0 X^2+X X 0 X^2+X 0 X^2+X X^2 0 X X X^2 X X 0 0 X 0 X^2+X X^2+X X X^2+X X X X X^2 X^2 X X^2 X^2 X 0 X X X^2+X X X 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 0 0 X^2 X^2 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 X^2 X^2 X^2 0 0 0 0 0 X^2 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 X^2 X^2 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 X^2 0 0 0 X^2 X^2 0 X^2 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 0 0 0 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 0 0 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 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 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 X^2 0 0 X^2 0 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 0 X^2 X^2 X^2 0 X^2 X^2 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 X^2 X^2 X^2 0 0 0 0 X^2 0 X^2 generates a code of length 46 over Z2[X]/(X^3) who´s minimum homogenous weight is 34. Homogenous weight enumerator: w(x)=1x^0+28x^34+42x^35+101x^36+80x^37+288x^38+246x^39+640x^40+412x^41+1334x^42+570x^43+2318x^44+722x^45+2851x^46+644x^47+2375x^48+608x^49+1349x^50+422x^51+603x^52+204x^53+246x^54+118x^55+86x^56+20x^57+40x^58+6x^59+16x^60+2x^61+7x^62+2x^64+1x^66+2x^68 The gray image is a linear code over GF(2) with n=184, k=14 and d=68. This code was found by Heurico 1.16 in 11.9 seconds.