The generator matrix
1 0 1 1 1 1 1
0 1 1 0 0 0 0
0 0 X 0 X 0 0
0 0 0 X X 0 0
0 0 0 0 X^2 0 0
0 0 0 0 0 X^2 0
generates a code of length 7 over Z2[X]/(X^3) who´s minimum homogenous weight is 2.
Homogenous weight enumerator: w(x)=1x^0+37x^2+32x^3+187x^4+96x^5+1055x^6+1280x^7+1055x^8+96x^9+187x^10+32x^11+37x^12+1x^14
The gray image is a linear code over GF(2) with n=28, k=12 and d=4.
This code was found by Heurico 1.16 in 0.00427 seconds.