The generator matrix

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

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+204x^22+124x^23+615x^24+456x^25+1057x^26+948x^27+1367x^28+976x^29+1125x^30+452x^31+532x^32+104x^33+163x^34+12x^35+45x^36+11x^38

The gray image is a code over GF(2) with n=112, k=13 and d=44.
This code was found by Heurico 1.16 in 65.9 seconds.