The generator matrix
1 1 1 1 X X X X
0 X 0 X 0 X X 0
0 0 X X X X 0 0
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+84x^4+416x^6+1046x^8+416x^10+84x^12+1x^16
The gray image is a linear code over GF(2) with n=32, k=11 and d=8.
This code was found by Heurico 1.16 in 0.00349 seconds.