The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+16x^3+87x^4+240x^5+336x^6+240x^7+87x^8+16x^9+1x^12

The gray image is a linear code over GF(2) with n=24, k=10 and d=6.
This code was found by Heurico 1.16 in 0.000618 seconds.