The generator matrix

 1  0  1  1  1 X+2  1  1 X+2  1  1  0  1  1  1  1  1  1  1  1  2  X  2  X  1  1  X  1
 0  1 X+1 X+2  3  1  0 X+1  1 X+2  3  1  2  X X+3  1  2  X X+3  1  1  1  1  1  0 X+2 X+2  0
 0  0  2  2  0  2  2  0  0  0  2  2  2  0  2  0  0  2  0  2  2  0  0  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+12x^26+32x^27+36x^28+32x^29+10x^30+3x^32+2x^38

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 0.00528 seconds.