The generator matrix

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

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+267x^6+1478x^8+5196x^10+9476x^12+9370x^14+5217x^16+1532x^18+212x^20+19x^22

The gray image is a linear code over GF(2) with n=26, k=15 and d=6.
As d=6 is an upper bound for linear (26,15,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 15.
This code was found by Heurico 1.11 in 0.704 seconds.