The generator matrix

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

generates a code of length 24 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+40x^20+8x^21+138x^22+184x^23+314x^24+184x^25+98x^26+8x^27+30x^28+10x^30+6x^32+2x^34+1x^40

The gray image is a code over GF(2) with n=192, k=10 and d=80.
This code was found by Heurico 1.16 in 0.016 seconds.