The generator matrix
1 1 1 1 X 1 1
0 X 0 0 X 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+29x^2+131x^4+607x^6+512x^7+607x^8+131x^10+29x^12+1x^14
The gray image is a linear code over GF(2) with n=28, k=11 and d=4.
This code was found by Heurico 1.16 in 0.00167 seconds.