The generator matrix

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

generates a code of length 15 over Z2[X]/(X^2) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+158x^10+343x^12+489x^14+576x^16+357x^18+101x^20+19x^22+3x^24+1x^26

The gray image is a linear code over GF(2) with n=30, k=11 and d=10.
As d=10 is an upper bound for linear (30,11,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 11.
This code was found by Heurico 1.16 in 29.1 seconds.