The generator matrix

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

generates a code of length 28 over Z2[X]/(X^2) who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+20x^21+54x^22+40x^23+100x^24+80x^25+56x^26+120x^27+64x^28+104x^29+124x^30+88x^31+83x^32+48x^33+8x^34+8x^35+4x^37+14x^38+8x^40

The gray image is a linear code over GF(2) with n=56, k=10 and d=21.
This code was found by Heurico 1.16 in 62.9 seconds.