The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  X
 0  X  0  0  0  0  0  X  0  X  0  0  X  X  0  X  X  X
 0  0  X  0  0  0  X  X  0  X  0  X  X  0  X  X  0  0
 0  0  0  X  0  0  X  0  0  X  X  X  0  X  0  X  0  X
 0  0  0  0  X  0  X  0  X  X  X  0  X  0  0  X  X  0
 0  0  0  0  0  X  X  0  X  0  0  0  X  X  X  X  0  X

generates a code of length 18 over Z2[X]/(X^2) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+78x^16+32x^20+16x^24+1x^32

The gray image is a linear code over GF(2) with n=36, k=7 and d=16.
As d=16 is an upper bound for linear (36,7,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 7.
This code was found by Heurico 1.16 in 0.00893 seconds.