The generator matrix

 1  0  0  1  1  1  0  1  1  X X+2  0  1  1 X+2  X  1  1  2  X  1  0  1  X  1 X+2  1  1
 0  1  0  1  X X+3  1  0 X+3  1  X  1  2 X+1  1  1  1  3  1  0  1  0  0  1  X  2  X  X
 0  0  1  1  1  0 X+3  X  X  1  1  X  1 X+1  X X+1  3  X X+3  1 X+1  0 X+1  2  0  1  2  1
 0  0  0  X  0 X+2 X+2  X  2  2 X+2 X+2  0  0 X+2  X  2 X+2  2 X+2 X+2  X  2  0  0  2  X  2
 0  0  0  0  2  0  0  2  2  2  2  2  2  2  0  2  0  0  0  0  0  0  0  2  2  2  0  0
 0  0  0  0  0  2  0  0  0  2  0  0  2  2  0  2  0  0  2  0  2  2  2  2  0  2  0  0
 0  0  0  0  0  0  2  2  0  2  2  2  2  0  0  2  2  2  2  0  2  2  0  2  2  0  0  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+60x^21+263x^22+498x^23+799x^24+1240x^25+1850x^26+2246x^27+2388x^28+2372x^29+1852x^30+1278x^31+758x^32+416x^33+254x^34+74x^35+20x^36+8x^37+5x^38+1x^40+1x^48

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 3.71 seconds.