The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1
0 X 0 0 0 0 0 0 0 0 0 X 0 0
0 0 X 0 0 0 0 0 0 0 0 X 0 0
0 0 0 X 0 0 0 0 0 0 0 X 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+55x^4+341x^8+627x^12+2048x^14+627x^16+341x^20+55x^24+1x^28
The gray image is a linear code over GF(2) with n=28, k=12 and d=4.
This code was found by Heurico 1.16 in 0.0504 seconds.