The generator matrix

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

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+30x^22+70x^23+104x^24+104x^25+97x^26+92x^27+78x^28+92x^29+80x^30+86x^31+64x^32+40x^33+41x^34+24x^35+8x^36+4x^37+8x^38+1x^40

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 0.0458 seconds.