The generator matrix

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

generates a code of length 24 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+54x^20+96x^22+215x^24+96x^26+42x^28+7x^32+1x^40

The gray image is a code over GF(2) with n=96, k=9 and d=40.
This code was found by Heurico 1.16 in 0.0138 seconds.