The generator matrix

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

generates a code of length 6 over Z2[X]/(X^3) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+9x^4+34x^5+45x^6+28x^7+6x^8+2x^9+3x^10

The gray image is a linear code over GF(2) with n=24, k=7 and d=8.
This code was found by Heurico 1.16 in 0.000115 seconds.