The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  X  1  1  1  1
 0  X  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  X  X  X  X  X  2  X X+2 X+2  X
 0  0  X  0  0  0  0  0  0  0  X X+2  X X+2 X+2  X X+2  0  0  X  2 X+2  2  2  X  X  2  0
 0  0  0  X  0  0  0  X X+2  X  X  X  0 X+2  X  0  0  X  X  X X+2 X+2  X  2  2  0  X  X
 0  0  0  0  X  0  X  X  X  2  0  0  2 X+2  X X+2  X  X  X X+2 X+2  X  0  2  X X+2  2  X
 0  0  0  0  0  X  X  2 X+2 X+2  0  X  X  X  2  0  X  X X+2  2 X+2  0  X X+2 X+2  2  X  X
 0  0  0  0  0  0  2  2  2  2  2  0  0  2  2  2  0  0  0  2  0  2  2  2  2  0  2  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+247x^20+558x^22+998x^24+1852x^26+2048x^27+4860x^28+2048x^29+2016x^30+1015x^32+532x^34+172x^36+34x^38+2x^40+1x^52

The gray image is a code over GF(2) with n=112, k=14 and d=40.
This code was found by Heurico 1.16 in 5.69 seconds.