The generator matrix
1 0 0 1 1 1 0 1 1 X 1 1 1
0 1 0 1 X X+1 1 0 X 0 1 1 X+1
0 0 1 1 1 0 X+1 X X+1 1 X+1 X+1 X+1
0 0 0 X 0 X X X X X 0 X 0
generates a code of length 13 over Z2[X]/(X^2) who´s minimum homogenous weight is 10.
Homogenous weight enumerator: w(x)=1x^0+11x^10+24x^11+24x^12+26x^13+14x^14+6x^15+7x^16+6x^17+7x^18+2x^19
The gray image is a linear code over GF(2) with n=26, k=7 and d=10.
This code was found by Heurico 1.16 in 0.000582 seconds.