The generator matrix
1 0 0 1 1 1 1
0 1 0 1 0 0 0
0 0 1 1 0 0 0
0 0 0 X 0 0 X^2
0 0 0 0 X 0 X^2
0 0 0 0 0 X X^2
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+71x^2+184x^3+805x^4+2592x^5+6291x^6+12880x^7+6291x^8+2592x^9+805x^10+184x^11+71x^12+1x^14
The gray image is a linear code over GF(2) with n=28, k=15 and d=4.
This code was found by Heurico 1.16 in 0.248 seconds.