The generator matrix

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

generates a code of length 28 over Z2[X]/(X^2) who´s minimum homogenous weight is 19.

Homogenous weight enumerator: w(x)=1x^0+24x^19+118x^20+190x^21+326x^22+406x^23+449x^24+608x^25+696x^26+784x^27+821x^28+852x^29+830x^30+676x^31+509x^32+352x^33+230x^34+152x^35+76x^36+46x^37+28x^38+6x^39+9x^40+2x^42+1x^44

The gray image is a linear code over GF(2) with n=56, k=13 and d=19.
This code was found by Heurico 1.16 in 2.57 seconds.