The generator matrix

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

generates a code of length 13 over Z2[X]/(X^2) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+97x^6+120x^7+478x^8+664x^9+1284x^10+1912x^11+2252x^12+2776x^13+2206x^14+1960x^15+1289x^16+648x^17+500x^18+104x^19+76x^20+8x^21+9x^22

The gray image is a linear code over GF(2) with n=26, k=14 and d=6.
As d=6 is an upper bound for linear (26,14,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 14.
This code was found by Heurico 1.16 in 1.7 seconds.