The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  0  1  1  1  2  2  1  X  X
 0  X  0  X  0  2  X X+2  0  2  X X+2  0  0  X  X  X  0  X  2  2  X X+2  0
 0  0  X  X  0  X X+2  2  0  X  X  0  0 X+2 X+2  2  X  2  0  2  0 X+2  2  0
 0  0  0  2  0  0  2  0  2  2  0  2  2  2  2  0  0  0  2  2  2  2  2  0
 0  0  0  0  2  2  2  2  2  2  0  2  0  0  2  2  2  0  0  0  0  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+51x^20+16x^21+107x^22+48x^23+105x^24+48x^25+62x^26+16x^27+26x^28+23x^30+8x^32+1x^36

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 0.0103 seconds.