The generator matrix

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

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+60x^20+118x^21+258x^22+450x^23+768x^24+1202x^25+1747x^26+2286x^27+2538x^28+2402x^29+1720x^30+1198x^31+805x^32+414x^33+226x^34+98x^35+50x^36+24x^37+14x^38+2x^40+3x^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 4.54 seconds.