The generator matrix

1 0 0 0 0 0 0 1 1 1 1
0 1 0 0 0 0 0 1 0 X 0
0 0 1 0 0 0 0 1 1 X+1 0
0 0 0 1 0 0 0 1 X 0 0
0 0 0 0 1 0 0 1 X X 0
0 0 0 0 0 1 0 1 X+1 1 0
0 0 0 0 0 0 1 1 X+1 X+1 0

generates a code of length 11 over Z2[X]/(X^2) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+113x^4+68x^5+553x^6+490x^7+1485x^8+2032x^9+1953x^10+3022x^11+1925x^12+2004x^13+1491x^14+518x^15+566x^16+56x^17+99x^18+2x^19+6x^20

The gray image is a linear code over GF(2) with n=22, k=14 and d=4.
As d=4 is an upper bound for linear (22,14,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 14.
This code was found by Heurico 1.10 in 0.047 seconds.