The generator matrix

 1  0  0  1  1  1  2  0  1  1  1  X  X  1  2  1  2  X  1  1  1  1  1  1
 0  1  0  0  1  1  1  X  2  3 X+2  1  1  3  X  0  1  2  X  3  3 X+3 X+3  0
 0  0  1  1  2  3  1  1  X X+2  1  1  0 X+3  1 X+1 X+1  1  X  0  X  2  2  3
 0  0  0  2  0  2  2  2  2  2  0  0  2  0  0  2  2  2  2  2  0  2  0  0

generates a code of length 24 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+138x^21+169x^22+214x^23+99x^24+160x^25+70x^26+88x^27+26x^28+38x^29+17x^30+2x^31+2x^32

The gray image is a code over GF(2) with n=96, k=10 and d=42.
This code was found by Heurico 1.11 in 5.63 seconds.