The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  X  1  1  X  X  1  X  X  1  1  1  1  1
 0  2  0  0  0  0  0  0  0  0  0  0  0  0  2  0  2  2  2  2  2  2  2  2  0  0  0  0
 0  0  2  0  0  0  0  0  0  0  0  0  2  0  0  2  2  2  2  2  0  0  0  2  0  0  0  0
 0  0  0  2  0  0  0  0  0  0  0  0  2  2  2  2  0  2  0  2  0  2  0  0  0  0  0  0
 0  0  0  0  2  0  0  0  0  0  0  0  2  2  2  0  2  0  0  2  0  0  2  2  0  0  0  0
 0  0  0  0  0  2  0  0  0  0  0  2  2  0  2  0  2  2  0  0  0  2  0  2  0  0  0  0
 0  0  0  0  0  0  2  0  0  0  0  2  0  0  0  2  0  2  0  2  2  2  0  2  0  0  0  0
 0  0  0  0  0  0  0  2  0  0  0  2  0  2  2  2  0  0  0  2  2  0  2  0  0  0  0  0
 0  0  0  0  0  0  0  0  2  0  0  2  0  2  2  0  0  2  2  2  0  0  0  2  0  0  0  0
 0  0  0  0  0  0  0  0  0  2  0  2  2  0  2  2  0  2  2  0  2  0  0  0  0  0  0  0
 0  0  0  0  0  0  0  0  0  0  2  2  2  2  0  2  0  2  0  0  0  0  2  2  0  0  0  0

generates a code of length 28 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+226x^16+104x^20+32x^22+784x^24+480x^26+4936x^28+480x^30+757x^32+32x^34+184x^36+152x^40+24x^44

The gray image is a code over GF(2) with n=112, k=13 and d=32.
This code was found by Heurico 1.16 in 1.17 seconds.