The generator matrix

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

generates a code of length 28 over Z2[X]/(X^2) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+66x^16+211x^18+96x^19+500x^20+480x^21+949x^22+1280x^23+1866x^24+2560x^25+2977x^26+3776x^27+3290x^28+3776x^29+2831x^30+2560x^31+1945x^32+1280x^33+1053x^34+480x^35+456x^36+96x^37+155x^38+58x^40+15x^42+10x^44+1x^46

The gray image is a linear code over GF(2) with n=56, k=15 and d=16.
This code was found by Heurico 1.16 in 21 seconds.