The generator matrix

 1  0  0  1  1  1 X+2  1  1  2  0  X  1  1  X  0  1  1 X+2  1  1  2  1  1
 0  1  0  0  1 X+1  1  2  0  X  1  1 X+1 X+3 X+2  X  1 X+2  1  1 X+3  1  3  0
 0  0  1 X+1 X+3  0 X+1  X  3  1 X+2  1 X+1  X  1  1  1  3  X  X X+2  3  3  2
 0  0  0  2  0  0  0  0  2  0  0  0  2  2  2  2  2  0  2  0  2  2  0  2
 0  0  0  0  2  2  0  2  2  2  2  2  2  0  2  0  0  2  0  0  2  0  0  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+113x^20+184x^21+370x^22+208x^23+375x^24+224x^25+270x^26+112x^27+127x^28+40x^29+14x^30+8x^32+2x^34

The gray image is a code over GF(2) with n=96, k=11 and d=40.
This code was found by Heurico 1.16 in 0.0517 seconds.