The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  0  1  2  1  2  X  X  1  1  2  1
 0  X  0  0  0  X X+2  X  0  2  X X+2  0  0  2  0  X  2 X+2  2 X+2  0  X  2
 0  0  X  0  X  X  X  2  0  2 X+2 X+2  X  2  0  X  0  X X+2 X+2  X  0  0  2
 0  0  0  X  X  2 X+2 X+2  0 X+2  2 X+2  X  X X+2 X+2 X+2 X+2  X X+2  0 X+2  X  2
 0  0  0  0  2  2  2  2  2  2  0  0  0  0  2  2  0  0  0  2  2  0  0  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+128x^20+238x^22+333x^24+196x^26+95x^28+14x^30+18x^32+1x^36

The gray image is a code over GF(2) with n=96, k=10 and d=40.
This code was found by Heurico 1.16 in 0.0587 seconds.