The generator matrix

 1  0  0  1  1  1  X  1  1  1  1  1  1  1  1  1  1  1  1  0  X  1
 0  1  0  X  1 X+1  1  X  0  0  1 X+1 X+1  X  1  0  X X+1  1  1  1  0
 0  0  1  1 X+1  X  1 X+1  1  X  1  0 X+1  0  X X+1  X  1  0  X  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+7x^20+18x^21+13x^22+12x^23+8x^24+2x^25+2x^26+1x^34

The gray image is a linear code over GF(2) with n=44, k=6 and d=20.
This code was found by Heurico 1.16 in 0.00101 seconds.