The generator matrix
1 0 0 0 1 1 1
0 1 0 0 X+1 0 0
0 0 1 0 1 0 0
0 0 0 1 1 0 0
0 0 0 0 X^2 0 0
0 0 0 0 0 X^2 0
0 0 0 0 0 0 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+79x^2+192x^3+909x^4+1920x^5+7715x^6+11136x^7+7715x^8+1920x^9+909x^10+192x^11+79x^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 0.214 seconds.