The generator matrix

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

generates a code of length 28 over Z2[X]/(X^2) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+8x^24+18x^25+18x^26+18x^27+14x^28+12x^29+12x^30+12x^31+7x^32+2x^33+1x^34+2x^35+2x^36+1x^50

The gray image is a linear code over GF(2) with n=56, k=7 and d=24.
This code was found by Heurico 1.16 in 0.00315 seconds.