The generator matrix

 1  0  0  0  0  0  1  1  1  0  1
 0  1  0  0  0  0  0  1  0  0  X
 0  0  1  0  0  0  0  1  1  1  X
 0  0  0  1  0  0  1  0  1  1  0
 0  0  0  0  1  0  1  0  0  0  X
 0  0  0  0  0  1  1  1  0  1  X
 0  0  0  0  0  0  X  0  0  X  0
 0  0  0  0  0  0  0  X  0  X  0
 0  0  0  0  0  0  0  0  X  X  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+124x^4+112x^5+721x^6+1056x^7+2710x^8+3984x^9+4636x^10+6080x^11+4636x^12+3984x^13+2710x^14+1056x^15+721x^16+112x^17+124x^18+1x^22

The gray image is a linear code over GF(2) with n=22, k=15 and d=4.
As d=4 is an upper bound for linear (22,15,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 15.
This code was found by Heurico 1.16 in 2.32 seconds.