The generator matrix
1 1 1 1 1 1 1 1
0 X^2 0 0 0 0 0 X^2
0 0 X^2 0 0 0 0 X^2
0 0 0 X^2 0 0 0 X^2
0 0 0 0 X^2 0 0 X^2
0 0 0 0 0 X^2 0 X^2
0 0 0 0 0 0 X^2 X^2
generates a code of length 8 over Z2[X]/(X^3) who´s minimum homogenous weight is 4.
Homogenous weight enumerator: w(x)=1x^0+28x^4+454x^8+28x^12+1x^16
The gray image is a linear code over GF(2) with n=32, k=9 and d=8.
This code was found by Heurico 1.16 in 0.000491 seconds.