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 X 0 X 0 X X^2 1 1 X^2 X X X 1 1 1 1 1 1 X 0 X 0 1 1 1 X X^2 X X^2 1 X X X X 1 1 1 1 X^2 X^2 0 0 X^2 X X 0 X 0 X X^2 1 1 X 1 1 X 1 1 X X
0 X 0 X^2+X X^2 X^2+X X^2 X 0 X^2+X 0 X^2+X X^2 X X^2 X 0 X^2+X 0 X^2+X X^2 X X^2 X X^2+X X X^2+X X X X 0 X^2+X X X 0 X^2 X^2 X 0 X^2+X X^2 X X^2+X X X^2+X X 0 X^2 0 X X X X X^2 0 X^2 0 X^2 X^2+X X X^2+X X 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2+X X X X 0 0 X^2 X^2 X^2 0 X^2+X X^2+X 0 0
0 0 X^2 X^2 X^2 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 0 X^2 0 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 0 X^2 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 X^2 0 X^2 0 X^2 0 X^2 0 0 0 X^2 X^2 0
generates a code of length 84 over Z2[X]/(X^3) who´s minimum homogenous weight is 84.
Homogenous weight enumerator: w(x)=1x^0+43x^84+10x^86+1x^88+6x^90+3x^92
The gray image is a linear code over GF(2) with n=336, k=6 and d=168.
This code was found by Heurico 1.16 in 0.409 seconds.