The generator matrix

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

generates a code of length 6 over Z2[X]/(X^3) who´s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+74x^2+64x^3+975x^4+1472x^5+3020x^6+1472x^7+975x^8+64x^9+74x^10+1x^12

The gray image is a linear code over GF(2) with n=24, k=13 and d=4.
This code was found by Heurico 1.16 in 0.0217 seconds.