The generator matrix

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

generates a code of length 19 over Z2[X]/(X^2) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+28x^16+40x^18+30x^20+24x^22+2x^24+2x^28+1x^32

The gray image is a linear code over GF(2) with n=38, k=7 and d=16.
As d=16 is an upper bound for linear (38,7,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 7.
This code was found by Heurico 1.16 in 0.00201 seconds.