The generator matrix
1 0 0 0 1 1 1 0
0 1 0 0 0 1 1 1
0 0 1 0 1 1 0 1
0 0 0 1 1 0 1 1
0 0 0 0 X 0 0 X
0 0 0 0 0 X 0 X
0 0 0 0 0 0 X X
generates a code of length 8 over Z2[X]/(X^2) who´s minimum homogenous weight is 4.
Homogenous weight enumerator: w(x)=1x^0+140x^4+448x^6+870x^8+448x^10+140x^12+1x^16
The gray image is a linear code over GF(2) with n=16, k=11 and d=4.
As d=4 is an upper bound for linear (16,11,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 11.
This code was found by Heurico 1.16 in 0.0068 seconds.