The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 0 X 0 X X X X X^2 X^2 1 1 1 1 X X 1 1 1 1 1 1 1 1 1 1 1
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 X^2+X X X^2+X X 0 X^2 X X X X 0 X^2 0 X^2 0 X^2 X^2+X X^2+X X X 0 0 X^2 X^2 X^2+X X^2+X X
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 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 0 0 0 X^2 X^2 0 0 X^2 X^2 0 0 X^2 X^2
generates a code of length 43 over Z2[X]/(X^3) who´s minimum homogenous weight is 42.
Homogenous weight enumerator: w(x)=1x^0+6x^42+44x^43+6x^44+1x^46+4x^47+1x^48+1x^62
The gray image is a linear code over GF(2) with n=172, k=6 and d=84.
This code was found by Heurico 1.16 in 0.0314 seconds.