The generator matrix

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

generates a code of length 6 over Z2[X]/(X^3) who´s minimum homogenous weight is 1.

Homogenous weight enumerator: w(x)=1x^0+28x^1+338x^2+2348x^3+10415x^4+29368x^5+46076x^6+29368x^7+10415x^8+2348x^9+338x^10+28x^11+1x^12

The gray image is a linear code over GF(2) with n=24, k=17 and d=2.
This code was found by Heurico 1.13 in 3.81e-009 seconds.