The generator matrix

 1  1  1  1  1  1  X  X
 0  X  0  0  0  X X^2 X^2
 0  0  X  0  X  X  X X^2
 0  0  0  X  X  0  0 X^2
 0  0  0  0 X^2  0 X^2 X^2
 0  0  0  0  0 X^2 X^2  0

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+83x^4+230x^6+256x^7+903x^8+256x^9+244x^10+69x^12+6x^14

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 0.00376 seconds.