The generator matrix

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

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+22x^4+84x^6+17x^8+4x^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 0.000148 seconds.