The generator matrix

 1  0  0  0  0  1  1  1  1  1  1  1  X  1
 0  1  0  0  0  1  X  X  1  1 X+1  0  1  0
 0  0  1  0  0  1  0  1 X+1  0  X  X  0  0
 0  0  0  1  0  1  0 X+1  X  1  X  1  1  0
 0  0  0  0  1  1 X+1 X+1  0  X  1  1  0  0
 0  0  0  0  0  X  X  0  X  0  X  0  0  0

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+55x^8+44x^9+143x^10+182x^11+185x^12+284x^13+235x^14+294x^15+228x^16+180x^17+125x^18+34x^19+43x^20+4x^21+9x^22+2x^23

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 0.0314 seconds.