The generator matrix

 1  0  0  1  1  1  0  1  1  1  1  1  0  X  0  1  0  X  X  X  1  1  0  1  1  0  X  X
 0  1  0  1  0  1  1  0  0  1 X+1  X  1  1  0  X  0  1  1  1  0  0  0  1  X  1  1  0
 0  0  1  1  1  0  1  0  1 X+1  X  1  X  1  1  1  1  X  1  1  0  X  1  1  1 X+1  1  X
 0  0  0  X  0  0  0  0  0  X  0  0  0  0  0  X  X  X  0  X  X  0  0  X  X  X  X  X
 0  0  0  0  X  0  0  0  0  0  0  0  X  X  X  X  X  0  0  0  X  0  0  X  0  X  0  X
 0  0  0  0  0  X  0  0  0  0  X  0  0  0  0  X  X  X  X  0  X  X  X  0  0  X  0  0
 0  0  0  0  0  0  X  0  0  0  0  0  0  X  0  0  0  0  X  X  X  X  0  X  X  X  X  0
 0  0  0  0  0  0  0  X  0  X  X  X  0  0  X  X  X  0  0  X  X  X  0  0  0  X  0  X
 0  0  0  0  0  0  0  0  X  0  0  X  X  X  X  X  0  X  X  0  0  X  0  0  0  X  X  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+132x^20+240x^22+571x^24+648x^26+895x^28+680x^30+585x^32+216x^34+106x^36+8x^38+11x^40+3x^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 1.01 seconds.