The generator matrix

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

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+71x^20+46x^24+8x^28+1x^32+1x^36

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 0.049 seconds.