The generator matrix

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

generates a code of length 28 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+76x^20+108x^21+301x^22+510x^23+901x^24+1304x^25+1683x^26+2154x^27+2297x^28+2196x^29+1651x^30+1298x^31+886x^32+544x^33+321x^34+70x^35+63x^36+8x^37+11x^38+1x^54

The gray image is a code over GF(2) with n=112, k=14 and d=40.
This code was found by Heurico 1.16 in 4.08 seconds.