The generator matrix

 1  0  1  1  1  0  1  1  0  1  X  1  1  1  1  2  1  1  1  X  1  1  X  1  X X+2  1  1
 0  1  1  0 X+1  1 X+3  0  1  3  1 X+2 X+2  X X+1  1  2 X+3 X+1  0  2  0  1 X+1  1  1  2  2
 0  0  X  0  0  0  0  X  X X+2  X  X  0  2 X+2  X  X  X  0  X  X  2  X X+2  0  X X+2  0
 0  0  0  X  0 X+2 X+2  X  X  X  2  X  2  X X+2  0  0  0  0 X+2  2  0  2 X+2 X+2 X+2  X  X
 0  0  0  0  2  0  0  0  0  0  2  2  2  0  0  2  0  0  2  2  2  0  2  2  0  0  0  0
 0  0  0  0  0  2  0  0  0  2  0  2  2  2  2  0  2  0  0  0  0  2  0  2  0  2  0  0
 0  0  0  0  0  0  2  0  2  0  0  0  2  2  2  2  2  0  0  0  2  2  2  0  2  2  0  2
 0  0  0  0  0  0  0  2  0  0  0  0  0  0  2  2  2  2  2  0  2  2  0  2  0  0  2  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+81x^20+76x^21+238x^22+330x^23+714x^24+1364x^25+1787x^26+2256x^27+2497x^28+2524x^29+1850x^30+1188x^31+761x^32+380x^33+196x^34+64x^35+37x^36+8x^37+24x^38+2x^39+4x^40+1x^42+1x^44

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 4.05 seconds.