The generator matrix

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

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+229x^12+542x^14+1351x^16+1876x^18+2150x^20+1280x^22+582x^24+140x^26+37x^28+2x^30+2x^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 1.1 seconds.