The generator matrix

 1  0  1  1  1  0  1  1  X  1 X+2  1  1  1  1  2  1  0  X  2  1 X+2  X  1  0  2  1  1
 0  1  1  0 X+1  1  X X+3  1 X+2  1  3  0  2 X+1  1 X+3  1  1  X  1  1  X  1  1  1 X+1 X+3
 0  0  X X+2  0 X+2  X X+2  X  0  2  0  2  X  0 X+2 X+2  0  X  X  X  2  X  X  2  X  0  X
 0  0  0  2  0  0  0  0  0  0  0  0  0  0  2  2  2  0  0  2  2  2  2  0  2  0  2  0
 0  0  0  0  2  0  0  0  0  0  0  2  0  0  2  0  0  2  2  2  0  2  0  2  0  2  2  0
 0  0  0  0  0  2  0  0  0  0  0  2  2  2  2  0  0  2  2  0  2  0  2  0  0  0  2  0
 0  0  0  0  0  0  2  0  0  0  0  0  0  2  2  2  2  2  2  0  0  2  2  2  2  0  0  2
 0  0  0  0  0  0  0  2  0  2  2  0  2  2  0  2  2  2  0  2  0  0  0  0  0  2  2  2
 0  0  0  0  0  0  0  0  2  0  0  2  2  2  2  2  0  2  0  2  2  0  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 20.

Homogenous weight enumerator: w(x)=1x^0+109x^20+24x^21+292x^22+328x^23+810x^24+1304x^25+1644x^26+2440x^27+2461x^28+2440x^29+1668x^30+1304x^31+859x^32+328x^33+228x^34+24x^35+99x^36+8x^38+10x^40+3x^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 3.88 seconds.