The generator matrix

 1  0  0  0  0  0  0  1  1  1  1  1  1
 0  1  0  0  0  0  0  0 X+1  0 X+1  1  X
 0  0  1  0  0  0  0  X  1 X+1  1  X  X
 0  0  0  1  0  0  0 X+1  0  1  X X+1  0
 0  0  0  0  1  0  0  1  X  X  0  X  1
 0  0  0  0  0  1  0  1  X  0 X+1 X+1  1
 0  0  0  0  0  0  1  1 X+1  X  X X+1  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+75x^6+168x^7+438x^8+672x^9+1276x^10+1976x^11+2324x^12+2512x^13+2282x^14+2072x^15+1265x^16+640x^17+460x^18+136x^19+68x^20+16x^21+3x^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 2.18 seconds.