The generator matrix

 1  0  1  1  1  2  1  1  0  1  1  0  X  1  1  1 X+2  1  1  1  1  2  1  1
 0  1  1  0 X+1  1  1  0  1  2 X+1  1  1  3 X+2  X  1  1 X+2 X+3  3  0  2  2
 0  0  X  0  0  2  0 X+2 X+2 X+2 X+2 X+2  2  2  0  2 X+2  X  X  0 X+2  X  X  0
 0  0  0  X  2  X X+2 X+2 X+2  2  X  2 X+2  2  0  X  2 X+2  X X+2  0  0 X+2  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+36x^20+110x^21+157x^22+162x^23+159x^24+128x^25+109x^26+106x^27+30x^28+2x^29+11x^30+2x^31+6x^32+3x^34+2x^35

The gray image is a code over GF(2) with n=96, k=10 and d=40.
This code was found by Heurico 1.16 in 0.0189 seconds.