The generator matrix

1 0 0 0 0 1 1 1 1 1 1 1 0 1
0 1 0 0 0 1 0 1 X X+1 X X 0 0
0 0 1 0 0 1 0 X 1 1 X+1 0 1 0
0 0 0 1 0 1 0 X+1 X+1 0 X X+1 1 0
0 0 0 0 1 1 X+1 1 0 X 1 0 X+1 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+54x^8+52x^9+140x^10+168x^11+190x^12+284x^13+240x^14+304x^15+223x^16+172x^17+124x^18+40x^19+42x^20+4x^21+8x^22+2x^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 1.10 in 0.016 seconds.