The generator matrix

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

generates a code of length 10 over Z2[X]/(X^2) who´s minimum homogenous weight is 3.

Homogenous weight enumerator: w(x)=1x^0+32x^3+189x^4+480x^5+1120x^6+2464x^7+4034x^8+5216x^9+5696x^10+5216x^11+4034x^12+2464x^13+1120x^14+480x^15+189x^16+32x^17+1x^20

The gray image is a linear code over GF(2) with n=20, k=15 and d=3.
As d=3 is an upper bound for linear (20,15,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 15.
This code was found by Heurico 1.11 in 0.0192 seconds.