The generator matrix

 1  0  0  0  0  0  1  1  1  1  0  1  X  1
 0  1  0  0  0  0  X  1 X+1  0  0  1  1  X
 0  0  1  0  0  0  0  0  1 X+1  1  X  X  X
 0  0  0  1  0  0  1 X+1  X X+1  X  X X+1  0
 0  0  0  0  1  0  1  X  X  1  1  0  0  0
 0  0  0  0  0  1  1  0 X+1  X  1  0  X  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+73x^8+150x^9+205x^10+212x^11+427x^12+746x^13+617x^14+472x^15+458x^16+362x^17+199x^18+84x^19+65x^20+22x^21+3x^22

The gray image is a linear code over GF(2) with n=28, k=12 and d=8.
As d=8 is an upper bound for linear (28,12,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 12.
This code was found by Heurico 1.16 in 0.134 seconds.