The generator matrix

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

generates a code of length 28 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+48x^22+258x^23+465x^24+812x^25+880x^26+1076x^27+1085x^28+1182x^29+882x^30+786x^31+370x^32+208x^33+92x^34+24x^35+15x^36+6x^37+2x^38

The gray image is a code over GF(2) with n=112, k=13 and d=44.
This code was found by Heurico 1.13 in 0.382 seconds.