The generator matrix
1 0 0 0 1 1 1 X 1 1 1 1 0 1 1
0 1 0 0 0 0 0 0 1 X+1 X+1 X 1 X X+1
0 0 1 0 0 1 1 1 1 1 X X+1 0 X+1 0
0 0 0 1 1 1 0 1 0 1 0 X 1 X+1 X+1
0 0 0 0 X 0 0 X X 0 X X X X X
0 0 0 0 0 X 0 X X 0 0 0 0 X X
0 0 0 0 0 0 X X 0 0 X 0 X 0 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+161x^10+324x^12+524x^14+565x^16+326x^18+132x^20+12x^22+2x^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 16.2 seconds.