The generator matrix
1 0 0 0 1 1 1 0 1 1 1 1 1 1 0 X 1 1 X
0 1 0 0 0 1 1 1 X X X+1 0 1 X+1 1 X 1 X 1
0 0 1 0 1 1 0 X+1 X 1 X+1 X 0 X+1 X+1 1 0 X+1 0
0 0 0 1 1 0 X+1 X+1 0 X X+1 1 X 1 1 X+1 X+1 X+1 1
0 0 0 0 X 0 X X X X 0 0 X X X 0 0 0 0
0 0 0 0 0 X 0 X 0 X 0 X X X 0 X X X 0
generates a code of length 19 over Z2[X]/(X^2) who´s minimum homogenous weight is 14.
Homogenous weight enumerator: w(x)=1x^0+90x^14+210x^16+219x^18+223x^20+181x^22+77x^24+21x^26+1x^28+1x^30
The gray image is a linear code over GF(2) with n=38, k=10 and d=14.
As d=14 is an upper bound for linear (38,10,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 10.
This code was found by Heurico 1.16 in 0.0368 seconds.