The generator matrix

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

generates a code of length 28 over Z2[X]/(X^2) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+62x^20+100x^21+196x^22+222x^23+267x^24+292x^25+326x^26+386x^27+331x^28+420x^29+361x^30+342x^31+266x^32+204x^33+158x^34+70x^35+63x^36+8x^37+14x^38+4x^39+2x^40+1x^46

The gray image is a linear code over GF(2) with n=56, k=12 and d=20.
This code was found by Heurico 1.16 in 0.649 seconds.