The generator matrix

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

generates a code of length 28 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+47x^20+36x^22+174x^24+412x^26+722x^28+412x^30+152x^32+36x^34+47x^36+8x^40+1x^48

The gray image is a code over GF(2) with n=112, k=11 and d=40.
This code was found by Heurico 1.16 in 0.102 seconds.