The generator matrix

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

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+9x^26+34x^27+45x^28+28x^29+6x^30+2x^31+2x^32+1x^54

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 0.00546 seconds.