The generator matrix

1 0 0 0 0 0 0 1 1 1 1 1 1
0 1 0 0 0 0 0 0 1 0 1 X+1 X
0 0 1 0 0 0 0 1 0 X X 0 1
0 0 0 1 0 0 0 1 X 0 X+1 X+1 0
0 0 0 0 1 0 0 1 X X+1 X 1 0
0 0 0 0 0 1 0 1 X+1 X 0 X+1 0
0 0 0 0 0 0 1 X 1 1 X+1 X 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+79x^6+168x^7+430x^8+680x^9+1276x^10+1912x^11+2332x^12+2680x^13+2274x^14+1880x^15+1273x^16+728x^17+460x^18+136x^19+60x^20+8x^21+7x^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 1.10 in 0.218 seconds.