The generator matrix
1 0 0 0 1 1 1
0 1 0 0 1 0 0
0 0 1 0 1 0 0
0 0 0 1 1 0 0
0 0 0 0 X 0 0
0 0 0 0 0 X 0
generates a code of length 7 over Z2[X]/(X^2) who´s minimum homogenous weight is 2.
Homogenous weight enumerator: w(x)=1x^0+29x^2+131x^4+351x^6+351x^8+131x^10+29x^12+1x^14
The gray image is a linear code over GF(2) with n=14, k=10 and d=2.
This code was found by Heurico 1.16 in 0.00123 seconds.