The generator matrix

 1  0  1  1  1 X+2  1  1  0  1  1  0  1  1  1  1  1  1  1  1 X+2 X+2  0  1  1  X  1  1
 0  1 X+1 X+2  1  1  0 X+1  1 X+2  3  1  0  3 X+2 X+1  0 X+2 X+1  3  1  1  1  0 X+1  0  0  0
 0  0  2  0  0  0  0  0  0  0  0  0  0  0  0  2  0  0  2  2  2  2  2  2  2  2  0  0
 0  0  0  2  0  0  0  0  0  0  0  0  0  0  2  0  2  2  0  0  2  2  2  2  2  2  2  2
 0  0  0  0  2  0  0  0  0  2  0  0  2  2  2  2  2  0  2  0  0  0  0  0  0  2  2  0
 0  0  0  0  0  2  0  0  0  2  0  2  2  0  0  0  2  2  2  2  0  0  0  2  2  2  0  2
 0  0  0  0  0  0  2  0  0  0  2  0  2  2  0  2  2  2  0  2  0  0  2  2  2  0  0  2
 0  0  0  0  0  0  0  2  0  2  2  0  2  0  2  2  2  0  2  0  2  2  2  0  2  0  0  0
 0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  0  0  2  0  0  2  0  0  0  2  0  2  2

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+75x^20+84x^22+64x^23+646x^24+448x^25+980x^26+1024x^27+1514x^28+1024x^29+1116x^30+448x^31+496x^32+64x^33+124x^34+75x^36+8x^40+1x^48

The gray image is a code over GF(2) with n=112, k=13 and d=40.
This code was found by Heurico 1.16 in 1.02 seconds.