The generator matrix
1 0 1 1 1 X 1 1 1 1 1
0 1 X+1 X 1 1 0 X X+1 1 0
generates a code of length 11 over Z2[X]/(X^2) who´s minimum homogenous weight is 10.
Homogenous weight enumerator: w(x)=1x^0+2x^10+8x^11+3x^12+1x^14+1x^18
The gray image is a linear code over GF(2) with n=22, k=4 and d=10.
This code was found by Heurico 1.16 in 0.000175 seconds.