The generator matrix

 1  0  1  1  1 X+2  1  1  0  1  1 X+2  1  1  2  1  1  X  X  1  1  X  0  2  X  1  1  X
 0  1 X+1 X+2  3  1  0 X+1  1 X+2  3  1  2 X+3  1  X  1  1  0  2  X X+2  1  X  1 X+3  3  0
 0  0  2  0  2  0  0  2  0  0  2  0  0  2  0  0  2  0  2  2  0  2  2  2  2  0  0  2
 0  0  0  2  2  2  2  2  2  0  0  0  2  0  2  0  2  0  2  2  2  2  0  0  2  0  2  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+48x^26+96x^27+40x^28+27x^30+32x^31+7x^32+4x^34+1x^46

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 0.0129 seconds.