The generator matrix

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

generates a code of length 22 over Z2[X]/(X^2) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+19x^18+44x^19+39x^20+28x^21+25x^22+32x^23+15x^24+12x^25+17x^26+9x^28+8x^29+3x^30+4x^31

The gray image is a linear code over GF(2) with n=44, k=8 and d=18.
This code was found by Heurico 1.16 in 0.00328 seconds.