The generator matrix

 1  0  0  0  0  1  1  1  0  1  1  X  1  1  1  X  0  0  1  X  1  X  1  1  1  1  1  1
 0  1  0  0  0  0  0  0  0  1  1  1 X+1  X  X  0  0  1  X  1 X+1  1  X X+1  X X+1 X+1  0
 0  0  1  0  0  0  1  1  1  X  1 X+1 X+1  1  0  1  1  X  X X+1 X+1 X+1  0  1  1  0  1  0
 0  0  0  1  0  1  1  0 X+1  X  0  X X+1  0 X+1 X+1  0 X+1  X  0  0  0  X  1  1 X+1 X+1  0
 0  0  0  0  1  1  0 X+1 X+1  1  X X+1 X+1  0  X  X  1  0  1  X  1 X+1 X+1  X X+1  X X+1  0
 0  0  0  0  0  X  0  X  X  X  0  X  X  X  X  X  0  X  X  X  X  X  0  X  0  0  X  0
 0  0  0  0  0  0  X  0  X  0  X  X  0  X  X  0  X  X  X  X  X  0  X  0  0  0  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+65x^20+102x^21+186x^22+222x^23+272x^24+286x^25+314x^26+384x^27+371x^28+422x^29+335x^30+360x^31+256x^32+194x^33+176x^34+56x^35+56x^36+20x^37+11x^38+2x^39+3x^40+1x^42+1x^50

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 0.633 seconds.