The generator matrix

 1  0  0  0  1  1  1  0  1  1  1  1  X  0  X  1  1  0  1  0  0  0  1  1  1  1  X  1
 0  1  0  0  0  0  0  1  1  1 X+1 X+1  1  X  1  X  0  1  1  1  1  0  X  1  1 X+1  X  1
 0  0  1  0  0  1  1  1  1  0  1  0  0  1  1  X X+1 X+1  X  X X+1  1 X+1  X X+1  X  1  1
 0  0  0  1  1  1  0  1  0 X+1  1  X  1  1  0  1  X X+1  X  1  0  X X+1 X+1  0 X+1 X+1  1
 0  0  0  0  X  0  0  0  0  0  X  0  0  0  0  X  0  X  X  0  X  X  X  0  0  X  X  0
 0  0  0  0  0  X  0  0  0  X  0  0  X  X  X  X  X  X  X  X  X  0  0  0  0  0  X  0
 0  0  0  0  0  0  X  0  0  0  0  X  X  X  X  X  X  X  0  X  0  X  X  0  0  X  X  X
 0  0  0  0  0  0  0  X  0  0  0  0  0  0  0  0  0  X  0  X  X  X  X  X  X  X  0  X
 0  0  0  0  0  0  0  0  X  X  X  X  X  X  0  0  X  0  0  0  X  0  X  0  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+234x^20+544x^22+1051x^24+1352x^26+1754x^28+1448x^30+1113x^32+472x^34+187x^36+24x^38+11x^40+1x^52

The gray image is a linear code over GF(2) with n=56, k=13 and d=20.
This code was found by Heurico 1.16 in 88.2 seconds.