The generator matrix

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

generates a code of length 22 over Z2[X]/(X^2) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+58x^20+32x^22+22x^24+14x^28+1x^32

The gray image is a linear code over GF(2) with n=44, k=7 and d=20.
As d=20 is an upper bound for linear (44,7,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 7.
This code was found by Heurico 1.16 in 0.00268 seconds.