The generator matrix

 1  0  1  1  1  2  1  1  2  1  2  1 X+2  1  2  1  X  1  1  1  1  1  1  1  1  X  X  1
 0  1  1  0  1  1 X+1  2  1 X+3  1  2  1  2  1 X+1  1 X+2  3 X+2  3 X+1  2  X  3  0 X+2  0
 0  0  X  0  0  0  0  X  X X+2  X  2  2 X+2  0  0  X  X X+2 X+2  2  2  2  0 X+2  2  0  0
 0  0  0  X  0  X  X  X X+2  X  2  2  X  2  2  0  X  0  0 X+2 X+2 X+2  0 X+2  0  X X+2  0
 0  0  0  0  X  2  X X+2 X+2  2  X  X X+2  2 X+2  2  2  X X+2  2  X  2  X  0  2  2 X+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+41x^22+138x^23+222x^24+346x^25+499x^26+526x^27+571x^28+582x^29+454x^30+344x^31+179x^32+78x^33+59x^34+30x^35+19x^36+2x^37+3x^38+2x^39

The gray image is a code over GF(2) with n=112, k=12 and d=44.
This code was found by Heurico 1.16 in 0.279 seconds.