The generator matrix

 1  0  0  0  1  1  1  0  1  1  1  1  X  1
 0  1  0  0  0  1  1  1  X  X  X X+1  1  0
 0  0  1  0  1  1  0  1  0  X  1  1  0  0
 0  0  0  1  1  0  1  1  1 X+1  X  1 X+1  0
 0  0  0  0  X  0  0  X  0  0  X  0  X  0
 0  0  0  0  0  X  0  X  X  X  0  0  0  0
 0  0  0  0  0  0  X  X  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+61x^8+50x^9+113x^10+180x^11+219x^12+254x^13+249x^14+344x^15+190x^16+142x^17+139x^18+52x^19+41x^20+2x^21+11x^22

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 0.0253 seconds.