The generator matrix

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

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+197x^18+823x^20+2009x^22+3812x^24+5912x^26+7085x^28+6122x^30+3915x^32+1965x^34+697x^36+173x^38+48x^40+6x^42+3x^44

The gray image is a linear code over GF(2) with n=56, k=15 and d=18.
This code was found by Heurico 1.16 in 57.3 seconds.