The generator matrix

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

generates a code of length 20 over Z2[X]/(X^2) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+432x^12+1416x^14+3672x^16+6604x^18+8428x^20+6716x^22+3744x^24+1348x^26+356x^28+44x^30+7x^32

The gray image is a linear code over GF(2) with n=40, k=15 and d=12.
As d=12 is an upper bound for linear (40,15,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 15.
This code was found by Heurico 1.16 in 88.2 seconds.