The generator matrix

 1  1  1  1  1  1  1  1  X  1  1  0  X  1  1  0  1  X  0  1  1  X  1  1  1  X  X  X
 0  X  0 X+2  0 X+2  0 X+2  X  0 X+2  X X+2 X+2  0  X X+2 X+2  X X+2  0 X+2  0  2  0 X+2  0  2
 0  0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  0  2
 0  0  0  2  0  0  0  0  0  0  0  0  0  2  0  0  2  2  0  0  2  0  2  2  2  0  2  2
 0  0  0  0  2  0  0  0  0  0  0  0  0  0  2  2  2  2  2  0  0  2  2  2  2  2  2  0
 0  0  0  0  0  2  0  0  0  0  2  0  2  2  2  2  0  0  0  0  2  0  2  2  0  0  2  0
 0  0  0  0  0  0  2  0  0  0  0  0  2  0  0  2  2  0  0  2  2  2  0  0  2  2  2  0
 0  0  0  0  0  0  0  2  0  0  2  2  0  0  2  2  0  0  2  2  0  0  2  2  0  2  0  0
 0  0  0  0  0  0  0  0  2  0  0  2  2  0  0  2  0  2  2  0  0  2  0  0  0  2  2  2
 0  0  0  0  0  0  0  0  0  2  0  2  2  2  2  0  2  2  0  2  2  0  0  2  0  2  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+188x^20+144x^22+64x^23+639x^24+576x^25+624x^26+1408x^27+904x^28+1408x^29+624x^30+576x^31+639x^32+64x^33+144x^34+188x^36+1x^56

The gray image is a code over GF(2) with n=112, k=13 and d=40.
This code was found by Heurico 1.16 in 61.7 seconds.