The generator matrix

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

generates a code of length 28 over Z2[X]/(X^2) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+39x^22+80x^23+86x^24+84x^25+96x^26+104x^27+93x^28+92x^29+78x^30+64x^31+63x^32+76x^33+40x^34+8x^35+10x^36+4x^37+3x^38+2x^40+1x^44

The gray image is a linear code over GF(2) with n=56, k=10 and d=22.
This code was found by Heurico 1.16 in 0.0457 seconds.