The generator matrix

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

generates a code of length 24 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+34x^22+58x^24+28x^26+4x^28+2x^30+1x^32

The gray image is a code over GF(2) with n=96, k=7 and d=44.
This code was found by Heurico 1.16 in 0.00435 seconds.