The generator matrix

 1  0  0  1  1  1  X  1  1  1  2 X+2  1  X  2 X+2  1 X+2  0  1  1  X  0  1  1  1  1  1
 0  1  0  1 X+2 X+3  1  0  0 X+1  1  1 X+3  X  X  0  X  1  1  3  X  1  0 X+2  1 X+1 X+1  0
 0  0  1  1 X+3 X+2  1 X+2 X+1 X+1  X X+1  X  1  1  1  X  0 X+1  0  1  1  1  0  X X+2  0  0
 0  0  0  2  0  0  0  0  0  2  2  2  0  2  0  2  2  0  0  0  2  2  0  0  2  0  2  0
 0  0  0  0  2  0  0  0  2  0  2  2  0  2  2  0  0  2  0  0  2  2  2  2  0  2  2  0
 0  0  0  0  0  2  0  0  0  0  2  2  2  2  0  2  2  2  0  0  0  0  2  2  2  2  0  0
 0  0  0  0  0  0  2  0  0  0  0  2  0  0  2  2  2  2  0  2  0  2  2  0  2  0  2  0
 0  0  0  0  0  0  0  2  2  2  2  0  2  2  0  0  2  2  2  0  0  2  0  0  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+32x^20+106x^21+179x^22+550x^23+674x^24+1470x^25+1631x^26+2454x^27+2158x^28+2514x^29+1616x^30+1506x^31+669x^32+506x^33+152x^34+98x^35+42x^36+12x^37+5x^38+8x^40+1x^42

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 3.14 seconds.