The generator matrix
1 0 1 1 1 0 1 1 0 1 1 0 1 1
0 1 1 0 1 1 0 1 1 0 X+1 1 0 0
0 0 X 0 0 0 0 0 0 0 0 X X X
0 0 0 X 0 0 0 0 0 0 X X X 0
0 0 0 0 X 0 0 0 0 0 X 0 X X
0 0 0 0 0 X 0 0 0 X 0 0 X X
0 0 0 0 0 0 X 0 0 X 0 X 0 X
0 0 0 0 0 0 0 X 0 X 0 X X 0
0 0 0 0 0 0 0 0 X X X 0 0 X
generates a code of length 14 over Z2[X]/(X^2) who´s minimum homogenous weight is 8.
Homogenous weight enumerator: w(x)=1x^0+85x^8+112x^10+544x^12+544x^14+579x^16+112x^18+64x^20+7x^24
The gray image is a linear code over GF(2) with n=28, k=11 and d=8.
As d=8 is an upper bound for linear (28,11,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 11.
This code was found by Heurico 1.16 in 0.0303 seconds.