The generator matrix

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

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+42x^20+8x^21+100x^22+56x^23+126x^24+56x^25+70x^26+8x^27+24x^28+12x^30+6x^32+2x^34+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 0.00908 seconds.