The generator matrix
1 0 1 1 1 X 1 1 1 1 1 1 1
0 1 X+1 X 1 1 0 X X+1 1 0 X 0
generates a code of length 13 over Z2[X]/(X^2) who´s minimum homogenous weight is 12.
Homogenous weight enumerator: w(x)=1x^0+3x^12+8x^13+2x^14+1x^18+1x^22
The gray image is a linear code over GF(2) with n=26, k=4 and d=12.
This code was found by Heurico 1.16 in 0.000254 seconds.