The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  X  X  1  X  X  X  1  X  X  1  X  X  X  X  X  X  X
 0  2  0  0  0  0  0  0  0  2  2  2  2  2  0  2  2  2  0  2  2  0  2  0  0  0  2  0
 0  0  2  0  0  0  2  2  2  2  2  2  2  2  2  2  0  2  2  0  0  2  0  0  2  0  2  0
 0  0  0  2  0  2  2  2  0  0  0  0  0  2  2  2  0  2  2  0  2  0  2  0  0  2  2  0
 0  0  0  0  2  2  0  2  2  0  2  0  2  2  0  2  0  0  2  2  0  2  2  2  0  2  0  0

generates a code of length 28 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+18x^26+92x^28+12x^30+3x^32+2x^42

The gray image is a code over GF(2) with n=112, k=7 and d=52.
This code was found by Heurico 1.16 in 0.1 seconds.