The generator matrix

 1  0  1  1  1 X+2  1  1  0  1  1 X+2  1  1  1  1  0  1 X+2  1  1  1 X+2  0
 0  1 X+1 X+2  1  1  0 X+1  1 X+2  3  1  0  2 X+2 X+1  1  3  1 X+2  3 X+3  1  1
 0  0  2  0  0  0  0  2  0  2  2  2  0  0  2  2  2  0  0  0  2  2  0  0
 0  0  0  2  0  0  2  2  0  2  0  2  0  2  2  0  0  2  2  0  0  2  0  0
 0  0  0  0  2  0  2  0  2  2  2  2  0  2  0  2  0  2  0  0  2  2  2  0
 0  0  0  0  0  2  0  2  2  2  0  2  2  2  0  2  0  0  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 20.

Homogenous weight enumerator: w(x)=1x^0+79x^20+304x^22+266x^24+304x^26+56x^28+13x^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 0.0196 seconds.