The generator matrix
1 0 1 X 1 1
0 1 1 0 0 0
0 0 X X 0 0
0 0 0 X^2 0 0
0 0 0 0 X^2 0
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+24x^2+16x^3+103x^4+176x^5+384x^6+176x^7+103x^8+16x^9+24x^10+1x^12
The gray image is a linear code over GF(2) with n=24, k=10 and d=4.
This code was found by Heurico 1.16 in 0.000388 seconds.