The generator matrix

1 0 0 0 0 0 1 1 1 1 1 0 1
0 1 0 0 0 0 0 1 1 X 0 1 0
0 0 1 0 0 0 0 1 X X+1 X+1 0 0
0 0 0 1 0 0 0 1 X+1 1 1 1 0
0 0 0 0 1 0 1 0 1 X X+1 0 0
0 0 0 0 0 1 1 X+1 1 0 1 1 0
0 0 0 0 0 0 X X 0 0 X 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+85x^6+70x^7+321x^8+316x^9+682x^10+922x^11+959x^12+1480x^13+959x^14+922x^15+682x^16+316x^17+321x^18+70x^19+85x^20+1x^26

The gray image is a linear code over GF(2) with n=26, k=13 and d=6.
This code was found by Heurico 1.10 in 0.063 seconds.