The generator matrix

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

generates a code of length 19 over Z2[X]/(X^2) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+204x^12+634x^14+1226x^16+1946x^18+2144x^20+1282x^22+556x^24+166x^26+28x^28+4x^30+1x^32

The gray image is a linear code over GF(2) with n=38, k=13 and d=12.
As d=12 is an upper bound for linear (38,13,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 13.
This code was found by Heurico 1.16 in 60.4 seconds.