The generator matrix

 1  0  0  1  1  1  X  2  1  1  1  2  1  2  0  1  1 X+2  1  2  1  1  1  1 X+2  1  1  1
 0  1  0  1  0 X+3  1  X X+2 X+2 X+3  1 X+3  1  1 X+2 X+1 X+2  3  1  2  X  X  1  1  X X+1 X+3
 0  0  1  1  1  0  1  1  X  1 X+1  1  X  0  1  0  1  1 X+2  0 X+2 X+1 X+3 X+1  X X+1  2  0
 0  0  0  X  0 X+2  2  X  2  X  0 X+2  X  X X+2 X+2  0 X+2  2  0 X+2  2  X X+2  0 X+2  0  0
 0  0  0  0  X  0  2 X+2 X+2  0  X X+2  X  2  0 X+2  2  2  X X+2  2  2 X+2  X  X  X X+2  X
 0  0  0  0  0  2  2  2  2  2  2  0  2  2  0  0  2  2  0  0  0  0  2  2  2  0  2  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+70x^21+238x^22+424x^23+818x^24+1304x^25+1758x^26+2252x^27+2524x^28+2360x^29+1871x^30+1344x^31+731x^32+352x^33+226x^34+76x^35+20x^36+10x^37+2x^38+2x^40+1x^46

The gray image is a code over GF(2) with n=112, k=14 and d=42.
This code was found by Heurico 1.16 in 3.82 seconds.