The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  X  1  X  X  1  1  1  X  X  X  X  1  1  1  1  1
 0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  0  0  0  0  0
 0  0  X  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  0  X  X  0  0  0  0  0  0  0
 0  0  0  X  0  0  0  0  0  0  0  0  X  X  X  0  0  X  X  0  X  X  0  0  0  0  0  0
 0  0  0  0  X  0  0  0  0  0  0  0  X  X  0  X  X  0  X  0  X  0  X  0  0  0  0  0
 0  0  0  0  0  X  0  0  0  0  0  X  0  X  0  X  X  X  X  0  0  X  0  0  0  0  0  0
 0  0  0  0  0  0  X  0  0  0  0  X  0  0  X  X  0  X  X  0  X  0  X  0  0  0  0  0
 0  0  0  0  0  0  0  X  0  0  0  X  0  X  X  0  0  X  0  X  0  X  X  0  0  0  0  0
 0  0  0  0  0  0  0  0  X  0  0  X  X  X  0  0  X  0  0  X  X  X  0  0  0  0  0  0
 0  0  0  0  0  0  0  0  0  X  0  X  X  0  0  X  X  X  0  X  0  0  X  0  0  0  0  0
 0  0  0  0  0  0  0  0  0  0  X  X  X  0  X  0  X  0  X  0  0  X  X  0  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+330x^16+224x^23+616x^24+176x^26+1120x^27+672x^31+77x^32+672x^34+32x^35+176x^42

The gray image is a linear code over GF(2) with n=56, k=12 and d=16.
This code was found by Heurico 1.16 in 0.654 seconds.