The generator matrix

 1  0  0  1  1  1 X+2  1  1  0  X  1  1  X  1  X X+2  1 X+2  1 X+2  2  1  1  1  2  1  1
 0  1  0  1  0 X+3  1  1 X+1  1  1 X+2 X+2  X X+3  0  2  1  1 X+3  1  0 X+1 X+3  3  1 X+2  0
 0  0  1  1  1  0  1  1  0  2  3 X+2  1  1  X  1  1 X+1  2  0 X+1  1  3  3 X+3  1  1  2
 0  0  0  X  0  0  0  2  X X+2 X+2 X+2  X  2 X+2  2 X+2  0  2 X+2  0 X+2 X+2  0 X+2  0  2  X
 0  0  0  0  X X+2 X+2  0 X+2  0 X+2  2  X  2 X+2 X+2  X  X X+2  0  2 X+2  X  0 X+2  2 X+2 X+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+87x^22+236x^23+484x^24+676x^25+884x^26+1172x^27+1175x^28+1098x^29+937x^30+684x^31+409x^32+192x^33+106x^34+36x^35+11x^36+2x^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 1.16 in 0.998 seconds.