The generator matrix

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

generates a code of length 6 over Z2[X]/(X^3) who´s minimum homogenous weight is 5.

Homogenous weight enumerator: w(x)=1x^0+8x^5+13x^6+8x^7+1x^8+1x^10

The gray image is a linear code over GF(2) with n=24, k=5 and d=10.
This code was found by Heurico 1.16 in 7.3e-005 seconds.