The generator matrix

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

generates a code of length 28 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+350x^21+792x^22+1938x^23+3015x^24+5656x^25+6719x^26+9264x^27+9383x^28+9916x^29+7283x^30+5452x^31+2820x^32+1832x^33+621x^34+368x^35+77x^36+38x^37+9x^38+2x^39

The gray image is a code over GF(2) with n=112, k=16 and d=42.
This code was found by Heurico 1.13 in 254 seconds.