The generator matrix

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

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+180x^20+128x^22+639x^24+640x^26+920x^28+640x^30+639x^32+128x^34+180x^36+1x^56

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 73 seconds.