The generator matrix
1 0 0 0 1 1 1 1 1 1 1 X 1 1
0 1 0 0 1 0 0 1 1 0 0 0 0 0
0 0 1 0 1 0 1 0 1 0 0 0 0 0
0 0 0 1 1 1 0 0 1 0 0 0 0 0
0 0 0 0 X 0 0 0 0 0 0 X 0 0
0 0 0 0 0 X 0 0 0 0 0 X 0 0
0 0 0 0 0 0 X 0 0 0 0 X 0 0
0 0 0 0 0 0 0 X 0 0 0 X 0 0
0 0 0 0 0 0 0 0 X 0 0 X 0 0
0 0 0 0 0 0 0 0 0 X 0 X 0 0
0 0 0 0 0 0 0 0 0 0 X X 0 0
generates a code of length 14 over Z2[X]/(X^2) who´s minimum homogenous weight is 4.
Homogenous weight enumerator: w(x)=1x^0+103x^4+336x^6+1605x^8+3392x^10+6995x^12+7904x^14+6995x^16+3392x^18+1605x^20+336x^22+103x^24+1x^28
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 1.6 seconds.