The generator matrix

1 0 0 0 0 1 1 1 X 1 1 X 1 1 1 0 X 1 1
0 1 0 0 0 0 0 X X 1 1 1 X+1 X X+1 X X X 1
0 0 1 0 0 1 X 1 1 0 X+1 X 0 X X 1 0 0 X+1
0 0 0 1 0 1 X+1 0 1 X X+1 0 1 1 X X+1 1 1 X
0 0 0 0 1 X 1 1 X+1 1 X+1 0 1 0 X X 1 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+54x^14+94x^15+115x^16+104x^17+78x^18+118x^19+118x^20+128x^21+82x^22+42x^23+52x^24+24x^25+10x^26+2x^27+2x^28

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 1.10 in 0.016 seconds.