The generator matrix

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

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+194x^22+538x^23+972x^24+1200x^25+1892x^26+2050x^27+2534x^28+2210x^29+2042x^30+1240x^31+847x^32+356x^33+192x^34+74x^35+30x^36+10x^37+2x^39

The gray image is a code over GF(2) with n=112, k=14 and d=44.
This code was found by Heurico 1.13 in 1.45 seconds.