The generator matrix

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

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+104x^21+451x^22+986x^23+1695x^24+2394x^25+3742x^26+4432x^27+5020x^28+4420x^29+3929x^30+2624x^31+1678x^32+730x^33+316x^34+160x^35+54x^36+16x^37+10x^38+6x^39

The gray image is a code over GF(2) with n=112, k=15 and d=42.
This code was found by Heurico 1.13 in 5.11 seconds.