The generator matrix

 1  0  1  1  1  0  1  1  1  1  1  1  X
 0  1  1  0  1  1  0  0  0  0  0  0  0
 0  0  X  0  0  0  0  0  0  0  0  0  X
 0  0  0  X  0  0  0  0  0  0  0  0  X
 0  0  0  0  X  0  0  0  0  0  0  0  X
 0  0  0  0  0  X  0  0  0  0  0  0  X
 0  0  0  0  0  0  X  0  0  0  0  0  X
 0  0  0  0  0  0  0  X  0  0  0  0  X
 0  0  0  0  0  0  0  0  X  0  0  0  X
 0  0  0  0  0  0  0  0  0  X  0  0  X
 0  0  0  0  0  0  0  0  0  0  X  0  X
 0  0  0  0  0  0  0  0  0  0  0  X  X

generates a code of length 13 over Z2[X]/(X^2) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+86x^4+72x^6+1003x^8+1696x^10+5796x^12+4080x^14+2983x^16+288x^18+358x^20+8x^22+13x^24

The gray image is a linear code over GF(2) with n=26, k=14 and d=4.
This code was found by Heurico 1.16 in 0.551 seconds.