The generator matrix

 1  0  0  1  1  1  0  1  1  X  1  1  1  1  1  X  1 X+2  1 X+2  1  1  2  2  X  0  X  1
 0  1  0  0  1  1  1  2 X+3  1 X+1  X  X  2 X+1  1  X  0  1  1  3 X+2  0  0  1  1  1  3
 0  0  1 X+1 X+3  0 X+1  X X+2  3  3  1 X+3  3 X+3 X+2  X  1  3  1  X  0  1  1  2 X+1  0 X+2
 0  0  0  2  0  0  0  2  2  2  2  2  0  2  0  2  0  0  0  0  2  2  2  0  2  0  0  0
 0  0  0  0  2  0  2  0  0  2  0  0  0  0  2  2  2  2  0  0  2  2  0  2  0  0  2  2
 0  0  0  0  0  2  0  0  0  2  0  0  0  2  2  0  0  2  0  2  0  0  2  2  2  2  2  2

generates a code of length 28 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+587x^24+912x^26+1166x^28+848x^30+527x^32+32x^34+18x^36+5x^40

The gray image is a code over GF(2) with n=112, k=12 and d=48.
This code was found by Heurico 1.16 in 23.1 seconds.