The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  0  2  0  X  1  2  0  X  1  1  2  2
 0  X  0  X  0  0  X X+2  0  2  X  0 X+2  2  X X+2  X  X  0 X+2  0  X  X X+2  0  2  X  X
 0  0  X  X  0 X+2  X  0  0  X  X  2  2  X X+2  0  0  X  X  0 X+2 X+2  2  0  2  0  X  X
 0  0  0  2  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  0  2  0  2  2  0  0  0  2
 0  0  0  0  2  0  0  0  0  0  0  2  0  2  2  2  2  0  0  0  2  0  0  2  2  2  2  2
 0  0  0  0  0  2  0  0  0  2  0  0  0  0  0  2  2  2  0  2  2  2  0  2  0  2  0  0
 0  0  0  0  0  0  2  0  0  0  2  0  0  0  0  2  2  0  2  0  2  2  2  0  2  2  0  0
 0  0  0  0  0  0  0  2  0  2  2  2  2  2  0  0  2  0  0  0  2  2  0  0  2  2  2  0
 0  0  0  0  0  0  0  0  2  0  0  0  2  2  2  2  0  0  2  2  0  0  2  2  2  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+123x^20+8x^21+278x^22+88x^23+720x^24+328x^25+1144x^26+600x^27+1589x^28+600x^29+1172x^30+328x^31+771x^32+88x^33+216x^34+8x^35+109x^36+6x^38+12x^40+3x^44

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 1.5 seconds.