The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  2  1  2  X  0  1  2  1  X  X  X  X
 0  X  0  0  0  0  0  0  0  X X+2  X  X X+2  X  2  2 X+2  X  0  0 X+2  X  X X+2  X  X X+2
 0  0  X  0  0  0  X X+2  X  0  0  0  X  X X+2  2  X  X  2  X  X  2  X  2  X  0  2  X
 0  0  0  X  0  X  X X+2  0  X  X  2  0  2 X+2  X  0  X  2  X X+2 X+2 X+2  X  0  X  2  X
 0  0  0  0  X  X  0 X+2  X  2 X+2 X+2  0 X+2  X X+2 X+2  0  X  2  X  0  X  X  X  2 X+2  2
 0  0  0  0  0  2  0  0  0  0  0  0  2  0  0  2  2  0  2  2  2  0  2  2  0  2  2  2
 0  0  0  0  0  0  2  0  2  2  0  2  0  0  2  2  2  2  0  0  2  0  0  2  0  0  2  2
 0  0  0  0  0  0  0  2  2  0  2  2  2  2  0  0  2  2  2  0  0  0  0  2  0  2  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+224x^20+590x^22+120x^23+1380x^24+704x^25+2344x^26+1112x^27+3102x^28+1472x^29+2532x^30+552x^31+1372x^32+128x^33+520x^34+8x^35+184x^36+30x^38+6x^40+2x^44+1x^48

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 5.89 seconds.