The generator matrix
1 0 0 1 1 1
0 1 0 0 0 X^2
0 0 1 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+20x^1+162x^2+708x^3+2159x^4+6440x^5+13788x^6+6440x^7+2159x^8+708x^9+162x^10+20x^11+1x^12
The gray image is a linear code over GF(2) with n=24, k=15 and d=2.
This code was found by Heurico 1.16 in 0.127 seconds.