The generator matrix

 1  0  0  0  1  1  1  0  1  1  1  1  X  X  X  1  1  1  0  1  1  1  X  X  X  1  1  1
 0  1  0  0  0  1  1  1  X  0 X+1 X+1  1  1  X  1  1  0  X  0  0  1  1  0  1  0 X+1  X
 0  0  1  0  1  1  0  1  0 X+1 X+1  X  X X+1  1  1  X X+1  X  X  1  0  0  1 X+1  0 X+1  0
 0  0  0  1  1  0  1  1  1  0  1  X X+1  0  1 X+1  1 X+1  1  0  X  0  0 X+1  X  X  1  1
 0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  0  X  X  X  X  0
 0  0  0  0  0  X  0  0  0  0  0  0  X  0  X  X  X  X  X  0  X  0  X  X  X  0  X  0
 0  0  0  0  0  0  X  0  0  0  0  0  0  X  X  X  X  X  X  X  0  X  0  0  X  0  0  0
 0  0  0  0  0  0  0  X  X  X  0  X  X  X  X  X  0  0  0  X  0  0  0  0  0  0  X  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+49x^20+90x^21+160x^22+224x^23+274x^24+310x^25+330x^26+390x^27+395x^28+410x^29+384x^30+342x^31+267x^32+194x^33+132x^34+66x^35+35x^36+20x^37+16x^38+2x^39+2x^40+2x^42+1x^44

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 0.618 seconds.