The generator matrix

 1  1  1  1  1  1
 0  X  0  0  0 X^2
 0  0  X  0  0  0
 0  0  0  X  0  0
 0  0  0  0  X  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+12x^1+66x^2+220x^3+495x^4+792x^5+5020x^6+792x^7+495x^8+220x^9+66x^10+12x^11+1x^12

The gray image is a linear code over GF(2) with n=24, k=13 and d=2.
This code was found by Heurico 1.16 in 0.0141 seconds.