The generator matrix

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

generates a code of length 28 over Z2[X]/(X^2) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+155x^18+955x^20+1865x^22+3891x^24+5818x^26+7222x^28+6026x^30+4017x^32+1815x^34+767x^36+189x^38+43x^40+4x^42

The gray image is a linear code over GF(2) with n=56, k=15 and d=18.
This code was found by Heurico 1.11 in 14.5 seconds.