The generator matrix

 1  0  1  1  1  X  1  1 X+2  1  2  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  1  1  2 X+1  1  X X+3  1 X+2  1 X+3 X+3  3  1  1  2  0 X+2 X+2  X  3  3  2  0 X+2  1 X+1
 0  0  X X+2  2 X+2  X X+2  0  0  X  2  X  0  2 X+2  0 X+2 X+2  2  0 X+2  2  X  2  X  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+52x^26+32x^27+92x^28+32x^29+40x^30+2x^32+4x^34+1x^48

The gray image is a code over GF(2) with n=112, k=8 and d=52.
This code was found by Heurico 1.16 in 0.00964 seconds.